]> 2026-07-15T16:34:00+00:00 Quaternion group 0 en 2 8 Term 2024-12-03T00:35:16Z 2460647.5244907 Quaternion group 0 Quaternion group#Underlying prime of p-group;2 2 0 Quaternion group#Order of a group;8 8 0 Quaternion group#Prime-base logarithm of order;3 3 0 Quaternion group#Exponent of a group;4 4 0 Quaternion group#Prime-base logarithm of exponent;2 2 0 Quaternion group#Nilpotency class;2 2 0 Quaternion group#Derived length;2 2 0 Quaternion group#Frattini length;2 2 0 Quaternion group#Minimum size of generating set;2 2 0 Quaternion group#Subgroup rank of a group;2 2 0 Quaternion group#Rank of a p-group;1 1 0 Quaternion group#Normal rank of a p-group;1 1 0 Quaternion group#Characteristic rank of a p-group;1 1 0 Quaternion group#Number of conjugacy classes;5 5 0 Quaternion group#Number of equivalence classes under real conjugacy;5 5 0 Quaternion group#Number of conjugacy classes of real elements;5 5 0 Quaternion group#Number of equivalence classes under rational conjugacy;5 5 0 Quaternion group#Number of conjugacy classes of rational elements;5 5 0 Quaternion group#Number of subgroups;6 6 0 Quaternion group#Number of conjugacy classes of subgroups;6 6 0 Quaternion group#Number of normal subgroups;6 6 0 Quaternion group#Number of automorphism classes of subgroups;4 4 0 Quaternion group#8;4 8 4 0 Quaternion group#8;5 8 5 0 1 plainlist 2 [[Specific information about::Quaternion group]] Quaternion group# QUERY68ea9b8945579df6de31ff5c430ab2e4 0 2 plainlist 3 [[Fact about.Page::Quaternion group]] Quaternion group# QUERY071970f7e84387cad46c4bca35f3e04e 0 2 plainlist 4 [[Fact about.Page::Quaternion group]] [[Category:Group property satisfactions]] Quaternion group# QUERY4d1877d99f7e66d05b0a5192c64d0bfc 0 2 plainlist 4 [[Fact about.Page::Quaternion group]] [[Category:Subgroup property satisfactions]] Quaternion group# QUERY487aeb2077a31f26bd0ac8b49c534eb6 0 2 plainlist 4 [[Fact about.Page::Quaternion group]] [[Category:Group property dissatisfactions]] Quaternion group# QUERY1846eda7299ee493a3e95a4cb1c8ae28 0 1 plainlist 4 [[Page class::Term]] [[Particular example::Quaternion group]] Quaternion group# QUERYf2743deac2a80171c5da8d92523af4c0 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Group properties]] Quaternion group# QUERY83f199f8b38aad469d2f4e6e7c7033a7 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Subgroup properties]] Quaternion group# QUERYa06abb9e1cfe600ee0fd5c1b25188889 0 1 plainlist 4 [[Particular example::Quaternion group]] [[Page class::Fact]] Quaternion group# QUERY7ee2131a16415c74ab8b0279c44e5860 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Group property non-implications]] Quaternion group# QUERYb927c79e9223845e1febdb45c9452879 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Subgroup property non-implications]] Quaternion group# QUERYe5c9207d3b705776220f089ea4c46e59 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Group metaproperty dissatisfactions]] Quaternion group# QUERY80f696b0520cd309b7f5f17da3cc375e 0 1 plainlist 3 [[Particular example::Quaternion group]] [[Category:Subgroup metaproperty dissatisfactions]] Quaternion group# QUERY82d013e3e8dffa20ecba43b184e46006 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Quaternion group# QUERY244130006d3535f90b4aa96a9c15968f 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERY5f4dd424107b030b995160dffd737ed1 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::4]]</q> ]] Quaternion group# QUERYfdcc45a6b524615968b7392891c478e0 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Quaternion group# QUERY807cf5389ccdcdc8ab9c8c46e8a74f6a 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Quaternion group# QUERY0b592f5378c67e72b4b38b061c2bb441 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::2]]</q> ]] Quaternion group# QUERY9988f417f8a610eaad43ece533289516 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> ]] Quaternion group# 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> ]] Quaternion group# QUERYf84e051b0dec95190cef070787d11e00 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Nilpotency class]] [[Number::2]]</q> ]] Quaternion group# 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> ]] Quaternion group# 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> ]] Quaternion group# QUERYbbe8a89a14e0f9c76173677c44b41117 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] Quaternion group# 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> ]] Quaternion group# 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> ]] Quaternion group# QUERY2615cc356c4e084cd0d9623b5b94db72 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::2]]</q> ]] Quaternion group# 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> ]] Quaternion group# 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> ]] Quaternion group# QUERYc492696730fdea506e1f8e7ad2f29ce9 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] Quaternion group# 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> ]] Quaternion group# 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> ]] Quaternion group# QUERY85601f1b41e6ce18460a2b2641a3a340 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] Quaternion group# QUERY2efb9d62dc2164771a85458ee7bafc0e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Quaternion group# QUERY4ce043ffbce6572c5c669a6defcea0dd 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Quaternion group# QUERYab23b0033026da68557ac1c994306c95 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] Quaternion group# QUERYd65fed11302674b9df97d1deff586a48 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::8]]</q> ]] Quaternion group# QUERYd8262c6efa7686bd4a19b6492994fe1b 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::3]]</q> ]] Quaternion group# QUERYcaba2744a2fac4e5958746b020dab318 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] Quaternion group# QUERYb2316714cd5b623271a238c70af90e1e 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> ]] Quaternion group# 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> ]] Quaternion group# QUERYca530b1951edcebc3202e0c22f5a7a53 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERYe3a44eae33d649a4bb0eb3bfc1f9f867 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::5]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERY75d69462d5799dcaf3bb94ff43520f79 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::5]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERYd081b538031bd0e8611205255e4aecbe 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of real elements]] [[Number::5]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERY63ee7d1e1144a7513885c7e86296ffe4 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::5]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERYeeea6d9c28131bab05c201eacc3fe638 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of rational elements]] [[Number::5]]</q> ]] Quaternion group# 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> ]] Quaternion group# QUERY95bc5e3e4882104ed92d4572364d2bfd 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of normal subgroups]] [[Number::6]]</q> ]] Quaternion group# QUERY86bbb9de4cdb7e480897a69e6781aec3 0 0 plainlist 1 [[:Groups of order 8]] Quaternion group# QUERY04c954a824b60a32b2734b908e7a5906 Quotient group need not be isomorphic to any subgroup 0 en Quotient group need not be isomorphic to any subgroup Ambivalent not implies strongly ambivalent 0 en Ambivalent not implies strongly ambivalent Nilpotent not implies abelian 0 en Nilpotent not implies abelian Rational not implies rational-representation 0 en Rational not implies rational-representation Endomorphism structure of quaternion group 0 en Endomorphism structure of quaternion group Second cohomology group for trivial group action of Q8 on Z2 0 en Second cohomology group for trivial group action of Q8 on Z2 Particular example 132 en Particular example Specific information about 132 en Specific information about