← Prev (#72219521) Next (#72219523) →
GO−(4,𝔽4) #72219522
Aliases
Splittings
Subgroups
47 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Permutation generators:
(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,34)(33,35)(36,38)(37,39)(40,42)(41,43)(44,46)(45,47)(48,51)(49,50)(52,55)(53,54)(56,59)(57,58)(60,63)(61,62)(64,69)(65,68)(66,71)(67,70)(72,77)(73,76)(74,79)(75,78)(80,84)(81,85)(82,86)(83,87)(88,92)(89,93)(90,94)(91,95)(96,103)(97,102)(98,101)(99,100)(104,111)(105,110)(106,109)(107,108)(112,118)(113,119)(114,116)(115,117)(120,126)(121,127)(122,124)(123,125)(128,138)(129,139)(130,136)(131,137)(132,142)(133,143)(134,140)(135,141)(144,155)(145,154)(146,153)(147,152)(148,159)(149,158)(150,157)(151,156)(160,168)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(176,185)(177,184)(178,187)(179,186)(180,189)(181,188)(182,191)(183,190)(192,207)(193,206)(194,205)(195,204)(196,203)(197,202)(198,201)(199,200)(208,222)(209,223)(210,220)(211,221)(212,218)(213,219)(214,216)(215,217)(224,237)(225,236)(226,239)(227,238)(228,233)(229,232)(230,235)(231,234)(240,252)(241,253)(242,254)(243,255)(244,248)(245,249)(246,250)(247,251);(16,18)(17,19)(20,22)(21,23)(24,26)(25,27)(28,30)(29,31)(32,35)(33,34)(36,39)(37,38)(40,43)(41,42)(44,47)(45,46)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,75)(65,74)(66,73)(67,72)(68,79)(69,78)(70,77)(71,76)(80,89)(81,88)(82,91)(83,90)(84,93)(85,92)(86,95)(87,94)(96,104)(97,105)(98,106)(99,107)(100,108)(101,109)(102,110)(103,111)(112,122)(113,123)(114,120)(115,121)(116,126)(117,127)(118,124)(119,125)(128,141)(129,140)(130,143)(131,142)(132,137)(133,136)(134,139)(135,138)(144,159)(145,158)(146,157)(147,156)(148,155)(149,154)(150,153)(151,152)(160,174)(161,175)(162,172)(163,173)(164,170)(165,171)(166,168)(167,169)(176,188)(177,189)(178,190)(179,191)(180,184)(181,185)(182,186)(183,187)(192,198)(193,199)(194,196)(195,197)(200,206)(201,207)(202,204)(203,205)(208,212)(209,213)(210,214)(211,215)(216,220)(217,221)(218,222)(219,223)(224,229)(225,228)(226,231)(227,230)(232,237)(233,236)(234,239)(235,238)(240,247)(241,246)(242,245)(243,244)(248,255)(249,254)(250,253)(251,252);(4,5)(6,7)(8,10)(9,11)(12,15)(13,14)(20,21)(22,23)(24,26)(25,27)(28,31)(29,30)(36,37)(38,39)(40,42)(41,43)(44,47)(45,46)(52,53)(54,55)(56,58)(57,59)(60,63)(61,62)(64,82)(65,83)(66,80)(67,81)(68,87)(69,86)(70,85)(71,84)(72,88)(73,89)(74,90)(75,91)(76,93)(77,92)(78,95)(79,94)(96,114)(97,115)(98,112)(99,113)(100,119)(101,118)(102,117)(103,116)(104,120)(105,121)(106,122)(107,123)(108,125)(109,124)(110,127)(111,126)(128,163)(129,162)(130,161)(131,160)(132,166)(133,167)(134,164)(135,165)(136,169)(137,168)(138,171)(139,170)(140,172)(141,173)(142,174)(143,175)(144,179)(145,178)(146,177)(147,176)(148,182)(149,183)(150,180)(151,181)(152,185)(153,184)(154,187)(155,186)(156,188)(157,189)(158,190)(159,191)(192,241)(193,240)(194,243)(195,242)(196,244)(197,245)(198,246)(199,247)(200,251)(201,250)(202,249)(203,248)(204,254)(205,255)(206,252)(207,253)(208,225)(209,224)(210,227)(211,226)(212,228)(213,229)(214,230)(215,231)(216,235)(217,234)(218,233)(219,232)(220,238)(221,239)(222,236)(223,237);(4,6)(5,7)(8,11)(9,10)(12,13)(14,15)(20,22)(21,23)(24,27)(25,26)(28,29)(30,31)(36,38)(37,39)(40,43)(41,42)(44,45)(46,47)(52,54)(53,55)(56,59)(57,58)(60,61)(62,63)(64,97)(65,96)(66,99)(67,98)(68,103)(69,102)(70,101)(71,100)(72,106)(73,107)(74,104)(75,105)(76,108)(77,109)(78,110)(79,111)(80,113)(81,112)(82,115)(83,114)(84,119)(85,118)(86,117)(87,116)(88,122)(89,123)(90,120)(91,121)(92,124)(93,125)(94,126)(95,127)(128,178)(129,179)(130,176)(131,177)(132,180)(133,181)(134,182)(135,183)(136,185)(137,184)(138,187)(139,186)(140,191)(141,190)(142,189)(143,188)(144,162)(145,163)(146,160)(147,161)(148,164)(149,165)(150,166)(151,167)(152,169)(153,168)(154,171)(155,170)(156,175)(157,174)(158,173)(159,172)(192,211)(193,210)(194,209)(195,208)(196,213)(197,212)(198,215)(199,214)(200,216)(201,217)(202,218)(203,219)(204,222)(205,223)(206,220)(207,221)(224,243)(225,242)(226,241)(227,240)(228,245)(229,244)(230,247)(231,246)(232,248)(233,249)(234,250)(235,251)(236,254)(237,255)(238,252)(239,253);(16,18)(17,19)(20,22)(21,23)(24,26)(25,27)(28,30)(29,31)(32,35)(33,34)(36,39)(37,38)(40,43)(41,42)(44,47)(45,46)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,75)(65,74)(66,73)(67,72)(68,79)(69,78)(70,77)(71,76)(80,89)(81,88)(82,91)(83,90)(84,93)(85,92)(86,95)(87,94)(96,104)(97,105)(98,106)(99,107)(100,108)(101,109)(102,110)(103,111)(112,122)(113,123)(114,120)(115,121)(116,126)(117,127)(118,124)(119,125)(128,141)(129,140)(130,143)(131,142)(132,137)(133,136)(134,139)(135,138)(144,159)(145,158)(146,157)(147,156)(148,155)(149,154)(150,153)(151,152)(160,174)(161,175)(162,172)(163,173)(164,170)(165,171)(166,168)(167,169)(176,188)(177,189)(178,190)(179,191)(180,184)(181,185)(182,186)(183,187)(192,198)(193,199)(194,196)(195,197)(200,206)(201,207)(202,204)(203,205)(208,212)(209,213)(210,214)(211,215)(216,220)(217,221)(218,222)(219,223)(224,229)(225,228)(226,231)(227,230)(232,237)(233,236)(234,239)(235,238)(240,247)(241,246)(242,245)(243,244)(248,255)(249,254)(250,253)(251,252);(16,19)(17,18)(20,23)(21,22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Conjugacy classes & character table
16 conjugacy classes — view the full character table.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,34)(33,35)(36,38)(37,39)(40,42)(41,43)(44,46)(45,47)(48,51)(49,50)(52,55)(53,54)(56,59)(57,58)(60,63)(61,62)(64,69)(65,68)(66,71)(67,70)(72,77)(73,76)(74,79)(75,78)(80,84)(81,85)(82,86)(83,87)(88,92)(89,93)(90,94)(91,95)(96,103)(97,102)(98,101)(99,100)(104,111)(105,110)(106,109)(107,108)(112,118)(113,119)(114,116)(115,117)(120,126)(121,127)(122,124)(123,125)(128,138)(129,139)(130,136)(131,137)(132,142)(133,143)(134,140)(135,141)(144,155)(145,154)(146,153)(147,152)(148,159)(149,158)(150,157)(151,156)(160,168)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(176,185)(177,184)(178,187)(179,186)(180,189)(181,188)(182,191)(183,190)(192,207)(193,206)(194,205)(195,204)(196,203)(197,202)(198,201)(199,200)(208,222)(209,223)(210,220)(211,221)(212,218)(213,219)(214,216)(215,217)(224,237)(225,236)(226,239)(227,238)(228,233)(229,232)(230,235)(231,234)(240,252)(241,253)(242,254)(243,255)(244,248)(245,249)(246,250)(247,251), 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Finite Group Databasebeta