Cyclic group-3AZ2
type: Ontology
creation date: 2026-03-01T02:44:07+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Cyclic group:Z2
type: Subject
type: Category:Particular groups
type: Category:Cyclic groups
type: Category:General affine groups
type: Category:Symmetric groups
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ2
wiki namespace: 0
wiki page content language: en
importance rank: 1
member of family: Symmetric group
member of family: Symmetric group on finite set
member of family: Symmetric group of prime degree
member of family: Multiplicative group of a field
order: 2
page class: Term
satisfies property: Abelian group
satisfies property: Cyclic group
satisfies property: Nilpotent group
satisfies property: Supersolvable group
satisfies property: Solvable group
satisfies property: Group of prime order
satisfies property: Simple group
satisfies property: Rational-representation group
satisfies property: Rational group
satisfies property: Ambivalent group
satisfies property: Strongly ambivalent group
satisfies property: T-group
satisfies property: Schur-trivial group
satisfies property: Finite group
wiki page modification date: 2023-12-15T21:23:53Z
modification date#aux: 2460294.3915857
wiki page sort key: Cyclic group:Z2

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_7a13bee84178de3902ce9e3091c9d67e
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
wiki page sort key: Cyclic group:Z2#Underlying prime of p-group;2
number: 2
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Underlying_prime_of_p-2Dgroup

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_498de9139b506126afa7b9da75a208cc
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
wiki page sort key: Cyclic group:Z2#Order of a group;2
number: 2
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Order_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_fcd8579966de469bf6531995b7d80f24
type: Subject
master page: Cyclic group:Z2
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wiki page sort key: Cyclic group:Z2#Prime-base logarithm of order;1
number: 1
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Prime-2Dbase_logarithm_of_order

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_22339dd6ade16633e44db36dd33edd08
type: Subject
master page: Cyclic group:Z2
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wiki page sort key: Cyclic group:Z2#Max-length of a group;1
number: 1
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Max-2Dlength_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_170f499ed1c03b0b8b9eda41822ff859
type: Subject
master page: Cyclic group:Z2
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number: 1
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Chief_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_672419670a5cda1d6be51f8cc01f2839
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Composition_length

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_0d1587ed0abe9607fd239f3e60046d04
type: Subject
master page: Cyclic group:Z2
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Exponent_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_42e4ffd18b76c50168082be75b8b49d0
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number: 1
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_39772cad9c2b5e494b34989a9ae06e3b
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_9a3c8ff85d3c6e869b42c6464da3e13c
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_9a5dc1282b1b09b360dc482e8e3535d2
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_62ab9e8f2b256c289032ad709d645230
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_4f4519941e890d8757571a146467c8d3
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_4f2863a776d7b4d35f6a17cee5a56ced
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_0679d36259ea244f412235bdedf7a958
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_5e780daef61805c26486c89a21399bef
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_a2807c8fd98cfd6f5dc00ab3be57483b
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_5741a43352fe37b047be3514500ab0ac
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_0a86a0c2e5d2a194468f90bc0faf59c0
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_fff95c7fb701ed8c66be28672d5cfe81
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master page: Cyclic group:Z2
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_conjugacy_classes_of_subgroups

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_e8112465dc02e75a3b698cd185a31ffa
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_f3a0a3af43442ae7a1b38accdca3dfdc
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_08b742ac15617d6ea7d0841395258ac5
type: Subject
master page: Cyclic group:Z2
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb64e7ba83dccdba9568bbc24db639f49
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY4d283774fe941ad75ddb82f61e7f4e98
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query string: Fact about.Page::Cyclic group:Z2
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb013061d3e866d6d94ed26cfc3b90dbf
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb3f01d926cfa71098e7f3a612c77e50c
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY3043026e3c8ba815d8b603f817d883b8
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYbd8a7fd3884cc4c46783b43bdaaca079
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYa4a70ab943a330458dce7ca0c50db2fd
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY83a1383c0593ab8a6a503613dbf0232a
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY2a901353adca70ff0361ae9c63b8e2ec
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY37fdc181e2be7edbfabb6cdf9f7ab767
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY3a67de97ce511db6299578f62e09f029
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY6ea5c077bc97d25e4eb48aed355d3784
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY9aea2775927fdd85b5b89c7aa3f923f7
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY8c3bea0e36371df588fd11c5da3e61e7
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYe6cac204bad0a3460cdb2e16f9ada9f2
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY4c1f2e280b208f6f9f0fddd77ae87ddb
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY206217d61ff02ae7b3133c5588213cce
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYc97cac1f808340611547748f41941823
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY3c6b993c49d03cfb6e2d4956d672a7a4
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY230e8aa990a4318395e2637c19304995
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYec93d74d1f07b00354996d5b23184aba
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY0091efdd97b9090d1f2f2a24d3b16127
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY34454195f8f2791153ebb290f8bcd6ea
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY5d57fc3c65d7cb34f4e343f28b202254
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYd65fed11302674b9df97d1deff586a48
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query string: Rank of a p-group 1
wiki page sort key: Cyclic group:Z2# QUERYd65fed11302674b9df97d1deff586a48

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY0229a64d503ca5a9f91b4b733c053a9c
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Normal rank of a p-group 1 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERY0229a64d503ca5a9f91b4b733c053a9c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY9d9bd395e3e435e38e86d2ec58163980
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Normal rank of a p-group 1 Prime-base logarithm of order 1
wiki page sort key: Cyclic group:Z2# QUERY9d9bd395e3e435e38e86d2ec58163980

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb2316714cd5b623271a238c70af90e1e
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Normal rank of a p-group 1
wiki page sort key: Cyclic group:Z2# QUERYb2316714cd5b623271a238c70af90e1e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY669b085e000bd641e375ebb0535e7df2
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Characteristic rank of a p-group 1 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERY669b085e000bd641e375ebb0535e7df2

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY2b4d4811c88ee8615df02d08ebdd4178
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Characteristic rank of a p-group 1 Prime-base logarithm of order 1
wiki page sort key: Cyclic group:Z2# QUERY2b4d4811c88ee8615df02d08ebdd4178

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY37c9612d33f64cebf0b3fea5d32afd85
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Characteristic rank of a p-group 1
wiki page sort key: Cyclic group:Z2# QUERY37c9612d33f64cebf0b3fea5d32afd85

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb20b310494e481d3fabdef5aacb839de
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes 2 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERYb20b310494e481d3fabdef5aacb839de

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYb4c99c1b821e11ac25d84be9ad91fd5e
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes 2
wiki page sort key: Cyclic group:Z2# QUERYb4c99c1b821e11ac25d84be9ad91fd5e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYc5531f2d1b775302eed4ee9ba4a7099c
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of subgroups 2 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERYc5531f2d1b775302eed4ee9ba4a7099c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYc6f06b5179b28e4fc386646b5898cc5c
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of subgroups 2
wiki page sort key: Cyclic group:Z2# QUERYc6f06b5179b28e4fc386646b5898cc5c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYd220e11876d1135cad86ee44f9d60457
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes of subgroups 2 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERYd220e11876d1135cad86ee44f9d60457

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY322871afe7f2b371b8fb8272167ac116
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes of subgroups 2
wiki page sort key: Cyclic group:Z2# QUERY322871afe7f2b371b8fb8272167ac116

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY4a812b2e735ac02a0308bc275c76f8d4
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of equivalence classes under real conjugacy 2 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERY4a812b2e735ac02a0308bc275c76f8d4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY7175b50b08553b741dbbe4710f77794f
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of equivalence classes under real conjugacy 2
wiki page sort key: Cyclic group:Z2# QUERY7175b50b08553b741dbbe4710f77794f

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYc9d25ce59b8289657585bd1ee4aee9d7
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of equivalence classes under rational conjugacy 2 Order of a group 2
wiki page sort key: Cyclic group:Z2# QUERYc9d25ce59b8289657585bd1ee4aee9d7

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERYd90cfc0c840e31bd763cde326262aec7
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of equivalence classes under rational conjugacy 2
wiki page sort key: Cyclic group:Z2# QUERYd90cfc0c840e31bd763cde326262aec7

http://groupprops.subwiki.org/wiki/Special:URIResolver/Cyclic_group-3AZ2-23_QUERY2227adcd647787e16878b3583768fc1e
type: Subject
master page: Cyclic group:Z2
wiki namespace: 0
query depth: 0
query format: plainlist
query size: 1
query string: Groups of order 2
wiki page sort key: Cyclic group:Z2# QUERY2227adcd647787e16878b3583768fc1e

Normality is not transitive
type: Subject
page: https://groupprops.subwiki.org/wiki/Normality_is_not_transitive
wiki namespace: 0
wiki page content language: en
particular example: Cyclic group:Z2
wiki page sort key: Normality is not transitive

Homomorph-containing not implies no nontrivial homomorphism to quotient group
type: Subject
page: https://groupprops.subwiki.org/wiki/Homomorph-2Dcontaining_not_implies_no_nontrivial_homomorphism_to_quotient_group
wiki namespace: 0
wiki page content language: en
particular example: Cyclic group:Z2
wiki page sort key: Homomorph-containing not implies no nontrivial homomorphism to quotient group

Direct product of Z2 and Z14
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_product_of_Z2_and_Z14
wiki namespace: 0
wiki page content language: en
defining ingredient: Cyclic group:Z2
wiki page sort key: Direct product of Z2 and Z14

Center of dihedral group:D8
type: Subject
page: https://groupprops.subwiki.org/wiki/Center_of_dihedral_group-3AD8
wiki namespace: 0
wiki page content language: en
subgroup part: Cyclic group:Z2
wiki page sort key: Center of dihedral group:D8

Second cohomology group for trivial group action of V4 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_V4_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of V4 on Z2

Second cohomology group for trivial group action of Z2 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_Z2_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of Z2 on Z2

Second cohomology group for trivial group action of Q8 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_Q8_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of Q8 on Z2

Second cohomology group for trivial group action of direct product of Z4 and Z2 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_direct_product_of_Z4_and_Z2_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of direct product of Z4 and Z2 on Z2

Second cohomology group for trivial group action of Z4 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_Z4_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of Z4 on Z2
value: Cyclic group:Z2

Second cohomology group for trivial group action of D8 on Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Second_cohomology_group_for_trivial_group_action_of_D8_on_Z2
wiki namespace: 0
wiki page content language: en
specific information about: Cyclic group:Z2
wiki page sort key: Second cohomology group for trivial group action of D8 on Z2

Particular example
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AParticular_example
wiki namespace: 132
wiki page content language: en
wiki page sort key: Particular example

Defining ingredient
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ADefining_ingredient
wiki namespace: 132
wiki page content language: en
wiki page sort key: Defining ingredient

Subgroup part
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ASubgroup_part
wiki namespace: 132
wiki page content language: en
wiki page sort key: Subgroup part
type: wpg

Specific information about
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ASpecific_information_about
wiki namespace: 132
wiki page content language: en
wiki page sort key: Specific information about
type: wpg

Value
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AValue
wiki namespace: 132
wiki page content language: en
wiki page sort key: Value