]> 2026-06-29T12:57:36+00:00 Symmetric group:S3 0 en 1 6 Term 2026-01-10T01:48:03Z 2461050.5750347 Symmetric group:S3 0 Symmetric group:S3#Order of a group;6 6 0 Symmetric group:S3#Exponent of a group;6 6 0 Symmetric group:S3#Derived length;2 2 0 Symmetric group:S3#Minimum size of generating set;2 2 0 Symmetric group:S3#Subgroup rank of a group;2 2 0 Symmetric group:S3#Max-length of a group;2 2 0 Symmetric group:S3#Number of conjugacy classes;3 3 0 Symmetric group:S3#Number of equivalence classes under real conjugacy;3 3 0 Symmetric group:S3#Number of conjugacy classes of real elements;3 3 0 Symmetric group:S3#Number of equivalence classes under rational conjugacy;3 3 0 Symmetric group:S3#Number of conjugacy classes of rational elements;3 3 0 Symmetric group:S3#Number of subgroups;6 6 0 Symmetric group:S3#Number of conjugacy classes of subgroups;4 4 0 Symmetric group:S3#Number of normal subgroups;3 3 0 Symmetric group:S3#Number of automorphism classes of subgroups;4 4 0 Symmetric group:S3#6;1 6 1 0 1 plainlist 2 [[Specific information about::Symmetric group:S3]] Symmetric group:S3# QUERYea616da7b8d1c7dbfa87b7b59ceaa2b6 0 2 plainlist 3 [[Fact about.Page::Symmetric group:S3]] Symmetric group:S3# QUERYaf6926a3c70d307fb0545401071e2788 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S3]] [[Category:Group property satisfactions]] Symmetric group:S3# QUERY98d3986253f4f601c4245f34fa239a43 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S3]] [[Category:Subgroup property satisfactions]] Symmetric group:S3# QUERYb4e7e931dd5a78c374244d0608467a22 0 2 plainlist 4 [[Fact about.Page::Symmetric group:S3]] [[Category:Group property dissatisfactions]] Symmetric group:S3# QUERY48db02fdce3c60e7837668bc941a7b20 0 1 plainlist 4 [[Page class::Term]] [[Particular example::Symmetric group:S3]] Symmetric group:S3# QUERY3213594a2dd8c1b9b4af8dda6a89fe5b 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Group properties]] Symmetric group:S3# QUERYadc1ebfab5c5eaaf85f4a9ca1a681210 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Subgroup properties]] Symmetric group:S3# QUERYa72fb8ab61e895de96f1e7adf2da1113 0 1 plainlist 4 [[Particular example::Symmetric group:S3]] [[Page class::Fact]] Symmetric group:S3# QUERY9c82def6fba4c7d19bc6b6159d75f718 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Group property non-implications]] Symmetric group:S3# QUERY7ccaec7ac3fc550338d2f0d279425212 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Subgroup property non-implications]] Symmetric group:S3# QUERYb308cc0e07d642faf327a3d8a56bce71 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Group metaproperty dissatisfactions]] Symmetric group:S3# QUERYf84e1b9db58d9cc6f9004b70df183189 0 1 plainlist 3 [[Particular example::Symmetric group:S3]] [[Category:Subgroup metaproperty dissatisfactions]] Symmetric group:S3# QUERY73607e297f35ab04f2d04e505715e85c 0 1 plainlist 2 [[Member of family::Symmetric group on finite set]] Symmetric group:S3# QUERYd8a215079cc37ae0e8dc5b4dee03fcb5 0 1 plainlist 2 [[Member of family::Coxeter group]] Symmetric group:S3# QUERYe84534dc854595f3aa145417b6a3e6d1 0 1 plainlist 2 [[Member of family::Dihedral group]] Symmetric group:S3# QUERY770a47f95764b9bc06fe7d3cef78a553 0 1 plainlist 2 [[Member of family::General affine group of degree one over a finite field]] Symmetric group:S3# QUERY464de132a6f2f3409719b4eedc5067e2 0 1 plainlist 2 [[Member of family::General linear group]] Symmetric group:S3# QUERY3511fcea568e685b72316d696ccd58e2 0 1 plainlist 2 [[Member of family::Projective general linear group]] Symmetric group:S3# QUERY82a9a2d7afbaf3560bee8f04f864768f 0 1 plainlist 2 [[Member of family::Special linear group]] Symmetric group:S3# QUERYe20edf84aff93f161099c5a77ec438b1 0 1 plainlist 2 [[Member of family::General semilinear group]] Symmetric group:S3# QUERY9df47db20c1d6bce8887e27e90fb8d32 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY30154c84aa4f981732fc817777630094 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::6]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY34fa4697a864fcd30c465d0b428c3be0 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY12b3ac9c7f507ec5e53ba9dc7558388b 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY670eba9a05063a1c59e5f309add0a928 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Derived length]] [[Number::2]]</q> ]] Symmetric group:S3# QUERYcf6cefe50f06f227269d2acd21de1fe0 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::6]]</q> ]] Symmetric group:S3# QUERY9af72fa0e0a6fe85da018d3eb14c7f76 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::2]]</q> ]] Symmetric group:S3# 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::6]]</q> ]] Symmetric group:S3# QUERY56cedfdb73c8f5814a8e51140e66937c 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::2]]</q> ]] Symmetric group:S3# QUERY2efb9d62dc2164771a85458ee7bafc0e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Max-length of a group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY85a57d7ee327a4c3928bbf20e04ad2bc 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Max-length of a group]] [[Number::2]]</q> ]] Symmetric group:S3# QUERY80d0ef9140f5e1b4c0b5e2e2b99ced6c 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERYa86985341c32e03d48864183309ba839 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::3]]</q> ]] Symmetric group:S3# QUERYd5772cd0c154b124575741687fd77698 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERYbb9a6508444e8cfa57ad5ecc515f7b3e 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::3]]</q> ]] Symmetric group:S3# QUERY100a4281522e8d205c36552f6618f55e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of real elements]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY6fe06dd72d3d55f2b03bb993b47217e4 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of real elements]] [[Number::3]]</q> ]] Symmetric group:S3# QUERY54ed50d5d257d8310ff41a4d48bc888b 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERYc4d2cd79117c8c973d3ed51ec51e80e9 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::3]]</q> ]] Symmetric group:S3# QUERY3e9549def5152797affe3249b0f1a6e8 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of rational elements]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY6c5e593e7d1d675df81ea6201e6ecaf3 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of rational elements]] [[Number::3]]</q> ]] Symmetric group:S3# QUERY282fa30781dec06a76787b5534dabf9f 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of normal subgroups]] [[Number::3]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::6]]</q> ]] Symmetric group:S3# QUERY84bab39de83f7433bb0367ce65d19451 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of normal subgroups]] [[Number::3]]</q> ]] Symmetric group:S3# QUERYbff4421548198e5201962135e71005ed 0 0 plainlist 1 [[:Groups of order 6]] Symmetric group:S3# QUERY416654683b3f91b55b3d9d5d2b321070 Order-conjugate and Hall not implies order-dominating 0 en Order-conjugate and Hall not implies order-dominating Nilpotent not implies nilpotent automorphism group 0 en Nilpotent not implies nilpotent automorphism group CA not implies nilpotent 0 en CA not implies nilpotent Order-conjugate not implies order-dominating 0 en Order-conjugate not implies order-dominating Normal-isomorph-free not implies isomorph-free in finite 0 en Normal-isomorph-free not implies isomorph-free in finite Supersolvable not implies nilpotent 0 en Supersolvable not implies nilpotent Characteristic not implies characteristic-isomorph-free in finite 0 en Characteristic not implies characteristic-isomorph-free in finite Class two not implies abelian automorphism group 0 en Class two not implies abelian automorphism group Transitively normal not implies conjugacy-closed normal 0 en Transitively normal not implies conjugacy-closed normal Finite not implies composition factor-permutable 0 en Finite not implies composition factor-permutable Modular not implies permutable 0 en Modular not implies permutable Direct product of Z5 and S3 0 en Direct product of Z5 and S3 S3 in S5 0 en S3 in S5 Particular example 132 en Particular example Defining ingredient 132 en Defining ingredient Subgroup part 132 en Subgroup part