Quaternion group
type: Ontology
creation date: 2026-01-17T02:56:20+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Quaternion group
type: Subject
type: Category:Particular groups
type: Category:Dicyclic groups
page: https://groupprops.subwiki.org/wiki/Quaternion_group
wiki namespace: 0
wiki page content language: en
dissatisfies property: Abelian group
dissatisfies property: Rational-representation group
dissatisfies property: One-headed group
dissatisfies property: SC-group
dissatisfies property: Frobenius group
dissatisfies property: A-group
importance rank: 2
member of family: Fibonacci group
order: 8
page class: Term
satisfies property: Frattini-in-center group
satisfies property: Metacyclic group
satisfies property: Group of nilpotency class two
satisfies property: Nilpotent group
satisfies property: Supersolvable group
satisfies property: Solvable group
satisfies property: Rational group
satisfies property: Ambivalent group
satisfies property: T-group
satisfies property: Schur-trivial group
satisfies property: Finite group
satisfies property: Dedekind group
satisfies property: Monolithic group
satisfies property: Camina group
satisfies property: Group of prime power order
satisfies property: Directly indecomposable group
satisfies property: Centrally indecomposable group
satisfies property: Splitting-simple group
satisfies property: Maximal class group
satisfies property: Extraspecial group
satisfies property: Special group
satisfies property: Group in which every element is automorphic to its inverse
satisfies property: Group in which any two elements generating the same cyclic subgroup are automorphic
satisfies property: 2-Engel group
wiki page modification date: 2024-12-03T00:35:16Z
modification date#aux: 2460647.5244907
wiki page sort key: Quaternion group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_7a13bee84178de3902ce9e3091c9d67e
type: Subject
master page: Quaternion group
wiki namespace: 0
wiki page sort key: Quaternion group#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/Quaternion_group-23_930225c358a23a5ea0082283c195cf44
type: Subject
master page: Quaternion group
wiki namespace: 0
wiki page sort key: Quaternion group#Order of a group;8
number: 8
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Order_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_20b4f8754e0bd0bf5ec62335fc106b5d
type: Subject
master page: Quaternion group
wiki namespace: 0
wiki page sort key: Quaternion group#Prime-base logarithm of order;3
number: 3
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Prime-2Dbase_logarithm_of_order

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_f42957b3baa9fd46e2346363e6d6b8bd
type: Subject
master page: Quaternion group
wiki namespace: 0
wiki page sort key: Quaternion group#Exponent of a group;4
number: 4
page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Exponent_of_a_group

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_b7594cc9c4c42965bc9010436e2f1fbc
type: Subject
master page: Quaternion group
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number: 2
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_c4e61a452f53ec65ceb9e9252853b2bf
type: Subject
master page: Quaternion group
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotency_class

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_e25716f2c9902d61b874a5e945bcd4e1
type: Subject
master page: Quaternion group
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_a9f8371b564d5335b51770f5d17a422f
type: Subject
master page: Quaternion group
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http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_5e221dcc4544cb5197d6f466b985fadc
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master page: Quaternion group
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type: Subject
master page: Quaternion group
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Subgroup_rank_of_a_group

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master page: Quaternion group
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type: Subject
master page: Quaternion group
wiki namespace: 0
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_subgroups

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type: Subject
master page: Quaternion group
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master page: Quaternion group
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_normal_subgroups

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type: Subject
master page: Quaternion group
wiki namespace: 0
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page: http://groupprops.subwiki.org/wiki/Special:URIResolver/Number_of_automorphism_classes_of_subgroups

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_0a214a1fba50e276e1ae1bd3a18a9b34
type: Subject
master page: Quaternion group
wiki namespace: 0
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number: 8
text: 4

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master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Subgroup rank of a group 2
wiki page sort key: Quaternion group# QUERY2efb9d62dc2164771a85458ee7bafc0e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY4ce043ffbce6572c5c669a6defcea0dd
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Rank of a p-group 1 Order of a group 8
wiki page sort key: Quaternion group# QUERY4ce043ffbce6572c5c669a6defcea0dd

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYab23b0033026da68557ac1c994306c95
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Rank of a p-group 1 Prime-base logarithm of order 3
wiki page sort key: Quaternion group# QUERYab23b0033026da68557ac1c994306c95

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYd65fed11302674b9df97d1deff586a48
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Rank of a p-group 1
wiki page sort key: Quaternion group# QUERYd65fed11302674b9df97d1deff586a48

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYd8262c6efa7686bd4a19b6492994fe1b
type: Subject
master page: Quaternion group
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 8
wiki page sort key: Quaternion group# QUERYd8262c6efa7686bd4a19b6492994fe1b

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYcaba2744a2fac4e5958746b020dab318
type: Subject
master page: Quaternion group
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 3
wiki page sort key: Quaternion group# QUERYcaba2744a2fac4e5958746b020dab318

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYb2316714cd5b623271a238c70af90e1e
type: Subject
master page: Quaternion group
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: Quaternion group# QUERYb2316714cd5b623271a238c70af90e1e

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY11594b186d8a395b90a31456a4eb0b40
type: Subject
master page: Quaternion group
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 8
wiki page sort key: Quaternion group# QUERY11594b186d8a395b90a31456a4eb0b40

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYca530b1951edcebc3202e0c22f5a7a53
type: Subject
master page: Quaternion group
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 3
wiki page sort key: Quaternion group# QUERYca530b1951edcebc3202e0c22f5a7a53

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY37c9612d33f64cebf0b3fea5d32afd85
type: Subject
master page: Quaternion group
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: Quaternion group# QUERY37c9612d33f64cebf0b3fea5d32afd85

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYe3a44eae33d649a4bb0eb3bfc1f9f867
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes 5 Order of a group 8
wiki page sort key: Quaternion group# QUERYe3a44eae33d649a4bb0eb3bfc1f9f867

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY73f27a0f765d5240815037f97dd48bde
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes 5
wiki page sort key: Quaternion group# QUERY73f27a0f765d5240815037f97dd48bde

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY75d69462d5799dcaf3bb94ff43520f79
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of equivalence classes under real conjugacy 5 Order of a group 8
wiki page sort key: Quaternion group# QUERY75d69462d5799dcaf3bb94ff43520f79

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYe5533936f92f4799b842d094bff58b2c
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of equivalence classes under real conjugacy 5
wiki page sort key: Quaternion group# QUERYe5533936f92f4799b842d094bff58b2c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYd081b538031bd0e8611205255e4aecbe
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes of real elements 5 Order of a group 8
wiki page sort key: Quaternion group# QUERYd081b538031bd0e8611205255e4aecbe

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY6750760b157b95ec13a536758f487238
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes of real elements 5
wiki page sort key: Quaternion group# QUERY6750760b157b95ec13a536758f487238

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY63ee7d1e1144a7513885c7e86296ffe4
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of equivalence classes under rational conjugacy 5 Order of a group 8
wiki page sort key: Quaternion group# QUERY63ee7d1e1144a7513885c7e86296ffe4

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYf8c5b2593027f4cd70bfa8ece706f229
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of equivalence classes under rational conjugacy 5
wiki page sort key: Quaternion group# QUERYf8c5b2593027f4cd70bfa8ece706f229

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYeeea6d9c28131bab05c201eacc3fe638
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of conjugacy classes of rational elements 5 Order of a group 8
wiki page sort key: Quaternion group# QUERYeeea6d9c28131bab05c201eacc3fe638

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERYe42bf1d430e2a15fb2e05af20615efa0
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of conjugacy classes of rational elements 5
wiki page sort key: Quaternion group# QUERYe42bf1d430e2a15fb2e05af20615efa0

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY95bc5e3e4882104ed92d4572364d2bfd
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 10
query string: Number of normal subgroups 6 Order of a group 8
wiki page sort key: Quaternion group# QUERY95bc5e3e4882104ed92d4572364d2bfd

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY86bbb9de4cdb7e480897a69e6781aec3
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 2
query format: table
query size: 5
query string: Number of normal subgroups 6
wiki page sort key: Quaternion group# QUERY86bbb9de4cdb7e480897a69e6781aec3

http://groupprops.subwiki.org/wiki/Special:URIResolver/Quaternion_group-23_QUERY04c954a824b60a32b2734b908e7a5906
type: Subject
master page: Quaternion group
wiki namespace: 0
query depth: 0
query format: plainlist
query size: 1
query string: Groups of order 8
wiki page sort key: Quaternion group# QUERY04c954a824b60a32b2734b908e7a5906

Quotient group need not be isomorphic to any subgroup
type: Subject
page: https://groupprops.subwiki.org/wiki/Quotient_group_need_not_be_isomorphic_to_any_subgroup
wiki namespace: 0
wiki page content language: en
particular example: Quaternion group
wiki page sort key: Quotient group need not be isomorphic to any subgroup

Ambivalent not implies strongly ambivalent
type: Subject
page: https://groupprops.subwiki.org/wiki/Ambivalent_not_implies_strongly_ambivalent
wiki namespace: 0
wiki page content language: en
particular example: Quaternion group
wiki page sort key: Ambivalent not implies strongly ambivalent

Nilpotent not implies abelian
type: Subject
page: https://groupprops.subwiki.org/wiki/Nilpotent_not_implies_abelian
wiki namespace: 0
wiki page content language: en
particular example: Quaternion group
wiki page sort key: Nilpotent not implies abelian

Rational not implies rational-representation
type: Subject
page: https://groupprops.subwiki.org/wiki/Rational_not_implies_rational-2Drepresentation
wiki namespace: 0
wiki page content language: en
particular example: Quaternion group
wiki page sort key: Rational not implies rational-representation

Endomorphism structure of quaternion group
type: Subject
page: https://groupprops.subwiki.org/wiki/Endomorphism_structure_of_quaternion_group
wiki namespace: 0
wiki page content language: en
specific information about: Quaternion group
wiki page sort key: Endomorphism structure of quaternion group

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: Quaternion group
wiki page sort key: Second cohomology group for trivial group action of Q8 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

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