]> 2026-09-05T03:33:09+00:00 Symmetric group:S4 0 en 2 24 Term 2026-01-10T01:43:20Z 2461050.5717593 Symmetric group:S4 0 Symmetric group:S4#Order of a group;24 24 0 Symmetric group:S4#Exponent of a group;12 12 0 Symmetric group:S4#Derived length;3 3 0 Symmetric group:S4#Frattini length;1 1 0 Symmetric group:S4#Minimum size of generating set;2 2 0 Symmetric group:S4#Subgroup rank of a group;2 2 0 Symmetric group:S4#Max-length of a group;4 4 0 Symmetric group:S4#Composition length;4 4 0 Symmetric group:S4#Chief length;3 3 0 Symmetric group:S4#Number of subgroups;30 30 0 Symmetric group:S4#Number of conjugacy classes;5 5 0 Symmetric group:S4#Number of conjugacy classes of subgroups;11 11 0 Symmetric group:S4#24;12 24 12 0 1 plainlist 2 [[Specific information about::Symmetric group:S4]] Symmetric group:S4# QUERY107e1afaf27abd2b54010adc00f1bdb1 0 2 plainlist 3 [[Fact about.Page::Symmetric group:S4]] Symmetric group:S4# QUERYa354b8a4817e439b7316dbacfc4099c0 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S4]] [[Category:Group property satisfactions]] Symmetric group:S4# QUERY66ad828ae7d67d129c7dbb978a6eb752 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S4]] [[Category:Subgroup property satisfactions]] Symmetric group:S4# QUERYd9b1e0821c9ef6263b49db942a32d3bd 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S4]] [[Category:Group property dissatisfactions]] Symmetric group:S4# QUERYfc608116e6b1ec5a9bce9dc9e8ae7e2e 0 1 plainlist 4 [[Page class::Term]] [[Particular example::Symmetric group:S4]] Symmetric group:S4# QUERY1657698b1760927187a08bb967ff8809 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Group properties]] Symmetric group:S4# QUERYa9a75f5fa17ed845d420af1850d8954e 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Subgroup properties]] Symmetric group:S4# QUERY38dac736c00235f85ee98b46761fdbc4 0 1 plainlist 4 [[Particular example::Symmetric group:S4]] [[Page class::Fact]] Symmetric group:S4# QUERYf26ee598267970fbdff626070ceb47da 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Group property non-implications]] Symmetric group:S4# QUERYc6b7a9fe1add102116ea8dea77c21906 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Subgroup property non-implications]] Symmetric group:S4# QUERY99041a86afce8366df6833a01220baa6 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Group metaproperty dissatisfactions]] Symmetric group:S4# QUERY4841116140193fcb9ae17b8ff4c11ca2 0 1 plainlist 3 [[Particular example::Symmetric group:S4]] [[Category:Subgroup metaproperty dissatisfactions]] Symmetric group:S4# QUERY3cf5f36108b7575753fa5dee54ce6b9a 0 1 plainlist 2 [[Member of family::Symmetric group on finite set]] Symmetric group:S4# QUERYd8a215079cc37ae0e8dc5b4dee03fcb5 0 1 plainlist 2 [[Member of family::Coxeter group]] Symmetric group:S4# QUERYe84534dc854595f3aa145417b6a3e6d1 0 1 plainlist 2 [[Member of family::Von Dyck group]] Symmetric group:S4# QUERYe5d265551c981541962e6573e68ca290 0 1 plainlist 2 [[Member of family::Triangle group]] Symmetric group:S4# QUERY0f2fbde8a7d5ba3d57210e6273e166e2 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY2c46463cfb77735ea25aca71bff94574 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::12]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERYacd6782405b5c4ed7822d117a82e59e4 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::12]]</q> ]] Symmetric group:S4# QUERY8af81a31ec7a65623ad7b2ed21f8eafb 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY75e177f93cdca86380c19c4851b29bac 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::3]]</q> ]] Symmetric group:S4# QUERY86f0a963559c347bfb62bb5639b2c4bc 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY719861a83d4e97bddaaddb3e7b76e3e5 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::1]]</q> ]] Symmetric group:S4# QUERY3c6b993c49d03cfb6e2d4956d672a7a4 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::24]]</q> ]] Symmetric group:S4# QUERYc2b6b71218cc42f91e99e0ff6c1db56b 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] Symmetric group:S4# 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::24]]</q> ]] Symmetric group:S4# QUERY54da2ed4bf95f60bb3294ddabd59fb43 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] Symmetric group:S4# QUERY2efb9d62dc2164771a85458ee7bafc0e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Max-length of a group]] [[Number::4]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY74c6e8d9c72e1a5942e96a45abb41c1d 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Max-length of a group]] [[Number::4]]</q> ]] Symmetric group:S4# QUERY5026c0f2f993b37cc26bc1289364b5c4 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Composition length]] [[Number::4]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERYc27fbb6ed25854c668fe0499b04aff49 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Composition length]] [[Number::4]]</q> ]] Symmetric group:S4# QUERY98e023fac27cc6e8077e60ab8e628369 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Chief length]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY2136616b8ca5977c350203a2f7c6d2a5 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Chief length]] [[Number::3]]</q> ]] Symmetric group:S4# QUERYc50491b3f22ac65dd61e60c095661ec6 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of subgroups]] [[Number::30]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY6054319080231f9350113634ee52237c 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of subgroups]] [[Number::30]]</q> ]] Symmetric group:S4# QUERY8a239fa0592b9f9deb52905da4d31790 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::24]]</q> ]] Symmetric group:S4# QUERYe71ed69a665f2a303364684726dad64e 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::5]]</q> ]] Symmetric group:S4# QUERY73f27a0f765d5240815037f97dd48bde 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of subgroups]] [[Number::11]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::24]]</q> ]] Symmetric group:S4# QUERY2683b5391a92aada019db08987316c11 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of subgroups]] [[Number::11]]</q> ]] Symmetric group:S4# QUERYc8cc0777a476d5dc0c766e76a693ac1f 0 0 plainlist 1 [[:Groups of order 24]] Symmetric group:S4# QUERYaabc9b9e4c6f4aae05741ca3ac60abb2 Pronormal not implies NE 0 en Pronormal not implies NE 2-subnormal not implies hypernormalized 0 en 2-subnormal not implies hypernormalized Subgroups of all orders dividing the group order not implies supersolvable 0 en Subgroups of all orders dividing the group order not implies supersolvable Finite solvable not implies p-normal 0 en Finite solvable not implies p-normal Sylow not implies local divisibility-closed 0 en Sylow not implies local divisibility-closed Sylow not implies CDIN 0 en Sylow not implies CDIN P-solvable not implies Glauberman type for p 0 en P-solvable not implies Glauberman type for p Subgroups of all orders dividing the group order not implies Sylow tower 0 en Subgroups of all orders dividing the group order not implies Sylow tower Pronormal not implies join with any distinct conjugate is the whole group 0 en Pronormal not implies join with any distinct conjugate is the whole group S4 in S5 0 en S4 in S5 Element structure of symmetric group:S4 0 en Element structure of symmetric group:S4 Particular example 132 en Particular example Subgroup part 132 en Subgroup part Specific information about 132 en Specific information about