]> 2026-08-12T03:43:47+00:00 Dihedral group:D8 0 en 2 8 Term 2026-07-30T01:06:56Z 2461251.5464815 Dihedral group:D8 0 Dihedral group:D8#Underlying prime of p-group;2 2 0 Dihedral group:D8#Order of a group;8 8 0 Dihedral group:D8#Prime-base logarithm of order;3 3 0 Dihedral group:D8#Max-length of a group;3 3 0 Dihedral group:D8#Chief length;3 3 0 Dihedral group:D8#Composition length;3 3 0 Dihedral group:D8#Exponent of a group;4 4 0 Dihedral group:D8#Prime-base logarithm of exponent;2 2 0 Dihedral group:D8#Nilpotency class;2 2 0 Dihedral group:D8#Derived length;2 2 0 Dihedral group:D8#Frattini length;2 2 0 Dihedral group:D8#Fitting length;1 1 0 Dihedral group:D8#Minimum size of generating set;2 2 0 Dihedral group:D8#Subgroup rank of a group;2 2 0 Dihedral group:D8#Rank of a p-group;2 2 0 Dihedral group:D8#Normal rank of a p-group;2 2 0 Dihedral group:D8#Characteristic rank of a p-group;1 1 0 Dihedral group:D8#Number of conjugacy classes;5 5 0 Dihedral group:D8#Number of equivalence classes under real conjugacy;5 5 0 Dihedral group:D8#Number of conjugacy classes of real elements;5 5 0 Dihedral group:D8#Number of equivalence classes under rational conjugacy;5 5 0 Dihedral group:D8#Number of conjugacy classes of rational elements;5 5 0 Dihedral group:D8#Number of subgroups;10 10 0 Dihedral group:D8#Number of conjugacy classes of subgroups;8 8 0 Dihedral group:D8#Number of normal subgroups;6 6 0 Dihedral group:D8#Number of automorphism classes of subgroups;6 6 0 Dihedral group:D8#Number of characteristic subgroups;4 4 0 Dihedral group:D8#8;3 8 3 0 Dihedral group:D8#8;4 8 4 0 1 plainlist 2 [[Specific information about::Dihedral group:D8]] Dihedral group:D8# QUERY3b56a93cf1ce16e61190957e8f50ada9 0 2 plainlist 3 [[Fact about.Page::Dihedral group:D8]] Dihedral group:D8# QUERYa4d00b253459337249faa43d50f1bf51 0 2 plainlist 4 [[Fact about.Page::Dihedral group:D8]] [[Category:Group property satisfactions]] Dihedral group:D8# QUERYc2ca87e757617c54b0547c8eb244d82c 0 2 plainlist 4 [[Fact about.Page::Dihedral group:D8]] [[Category:Subgroup property satisfactions]] Dihedral group:D8# QUERY3c4f77cfd3876ff718312946115c1ac4 0 2 plainlist 4 [[Fact about.Page::Dihedral group:D8]] [[Category:Group property dissatisfactions]] Dihedral group:D8# QUERYb6159417142a6235fd49f90f9e4fa8c9 0 1 plainlist 4 [[Page class::Term]] [[Particular example::Dihedral group:D8]] Dihedral group:D8# QUERY33906dfe6d0d1857f6287b1c71aa5300 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Group properties]] Dihedral group:D8# QUERY458e36884939a51481496f0355f4228d 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Subgroup properties]] Dihedral group:D8# QUERYd871734c9b51073323746495ab81be2c 0 1 plainlist 4 [[Particular example::Dihedral group:D8]] [[Page class::Fact]] Dihedral group:D8# QUERY57aa50f555c3f7f845d72d56d58dee63 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Group property non-implications]] Dihedral group:D8# QUERYed85b566fc8541934eed20ca4d5cd968 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Subgroup property non-implications]] Dihedral group:D8# QUERY891da2b0e332c99d736897a29bba3c3f 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Group metaproperty dissatisfactions]] Dihedral group:D8# QUERYa93eb31b2060fd9494a0751f09f58554 0 1 plainlist 3 [[Particular example::Dihedral group:D8]] [[Category:Subgroup metaproperty dissatisfactions]] Dihedral group:D8# QUERY20a86dc8e5660c7ad4b08e4502f541ed 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY244130006d3535f90b4aa96a9c15968f 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERY39edbc839d97c2a3395c3ad20c3b88b6 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::4]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY5f4dd424107b030b995160dffd737ed1 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::4]]</q> ]] Dihedral group:D8# QUERYfdcc45a6b524615968b7392891c478e0 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Nilpotency class]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY386ff0d3814dc99000fb51040778c3a4 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Nilpotency class]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERYf84e051b0dec95190cef070787d11e00 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Nilpotency class]] [[Number::2]]</q> ]] Dihedral group:D8# QUERYce2a47fc34a8c5d87f34e4a19f3397b7 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY837e375058054c48efda5bdc54eec045 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERYbbe8a89a14e0f9c76173677c44b41117 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] Dihedral group:D8# QUERYcf6cefe50f06f227269d2acd21de1fe0 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERYa06c1d175334036752dfa35c5b411feb 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERY2615cc356c4e084cd0d9623b5b94db72 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::2]]</q> ]] Dihedral group:D8# QUERY69df6712acf76e0c909be6079422ec01 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY78a3be527c496c6e423aa0fad3566127 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERYc492696730fdea506e1f8e7ad2f29ce9 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] Dihedral group:D8# QUERYe750a6e6983602278a40c54230968a76 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY46da310d815d4eeb8f4fe8daf23bda79 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERY85601f1b41e6ce18460a2b2641a3a340 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] Dihedral group:D8# QUERY2efb9d62dc2164771a85458ee7bafc0e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY56a26d20c9f491c85cc51b5373cb295b 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERY7c8dad126200f45739ea315c44e9f8f1 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::2]]</q> ]] Dihedral group:D8# QUERY7970e37817a0a704a54f6168586e86cc 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY544d2a63182c4574f55cc816f4e01a1b 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERYfc40a66be2f174dc32be0f74af8137cf 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::2]]</q> ]] Dihedral group:D8# QUERYaca56bac9580082a624ab2142fe4ab36 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY11594b186d8a395b90a31456a4eb0b40 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Dihedral group:D8# QUERYca530b1951edcebc3202e0c22f5a7a53 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] Dihedral group:D8# QUERY37c9612d33f64cebf0b3fea5d32afd85 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::5]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERYe3a44eae33d649a4bb0eb3bfc1f9f867 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::5]]</q> ]] Dihedral group:D8# QUERY73f27a0f765d5240815037f97dd48bde 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::5]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY75d69462d5799dcaf3bb94ff43520f79 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::5]]</q> ]] Dihedral group:D8# QUERYe5533936f92f4799b842d094bff58b2c 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of real elements]] [[Number::5]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERYd081b538031bd0e8611205255e4aecbe 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of real elements]] [[Number::5]]</q> ]] Dihedral group:D8# QUERY6750760b157b95ec13a536758f487238 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::5]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY63ee7d1e1144a7513885c7e86296ffe4 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::5]]</q> ]] Dihedral group:D8# QUERYf8c5b2593027f4cd70bfa8ece706f229 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of rational elements]] [[Number::5]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERYeeea6d9c28131bab05c201eacc3fe638 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of rational elements]] [[Number::5]]</q> ]] Dihedral group:D8# QUERYe42bf1d430e2a15fb2e05af20615efa0 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of normal subgroups]] [[Number::6]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Dihedral group:D8# QUERY95bc5e3e4882104ed92d4572364d2bfd 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of normal subgroups]] [[Number::6]]</q> ]] Dihedral group:D8# QUERY86bbb9de4cdb7e480897a69e6781aec3 0 0 plainlist 1 [[:Groups of order 8]] Dihedral group:D8# QUERY04c954a824b60a32b2734b908e7a5906 Normality is not transitive 0 en Normality is not transitive Left-transitively WNSCDIN not implies normal 0 en Left-transitively WNSCDIN not implies normal Characteristically metacyclic not implies metacyclic derived series 0 en Characteristically metacyclic not implies metacyclic derived series Characteristic not implies fully invariant 0 en Characteristic not implies fully invariant 2-subnormal not implies automorph-permutable 0 en 2-subnormal not implies automorph-permutable Transitively normal not implies central factor 0 en Transitively normal not implies central factor Normal not implies normal-potentially characteristic 0 en Normal not implies normal-potentially characteristic Normal not implies central factor 0 en Normal not implies central factor Sylow not implies CDIN 0 en Sylow not implies CDIN Nilpotent automorphism group not implies abelian automorphism group 0 en Nilpotent automorphism group not implies abelian automorphism group Nilpotent not implies abelian 0 en Nilpotent not implies abelian Potentially characteristic not implies normal-potentially characteristic 0 en Potentially characteristic not implies normal-potentially characteristic Normal-extensible not implies normal 0 en Normal-extensible not implies normal Normal not implies left-transitively fixed-depth subnormal 0 en Normal not implies left-transitively fixed-depth subnormal Normal-isomorph-free not implies isomorph-free in finite 0 en Normal-isomorph-free not implies isomorph-free in finite Abelian normal not implies central 0 en Abelian normal not implies central Complemented normal not implies direct factor 0 en Complemented normal not implies direct factor Normal not implies normal-potentially relatively characteristic 0 en Normal not implies normal-potentially relatively characteristic Class two not implies abelian automorphism group 0 en Class two not implies abelian automorphism group Center of dihedral group:D8 0 en Center of dihedral group:D8 Subgroup structure of dihedral group:D8 0 en Subgroup structure of dihedral group:D8 Element structure of dihedral group:D8 0 en Element structure of dihedral group:D8 Second cohomology group for trivial group action of D8 on V4 0 en Second cohomology group for trivial group action of D8 on V4 Second cohomology group for trivial group action of D8 on Z4 0 en Second cohomology group for trivial group action of D8 on Z4 Second cohomology group for trivial group action of D8 on Z2 0 en Second cohomology group for trivial group action of D8 on Z2 Particular example 132 en Particular example Group part 132 en Group part Specific information about 132 en Specific information about