C₂×D₁₄₄₉₉ #72292592

order	57996
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₈₉₉₈
direct product	C₂×D₁₄₄₉₉

Splittings

Fitting	C₂×C₈₁×C₁₇₉ ⋊ C₂
derived, Hall	C₈₁×C₁₇₉ ⋊ C₂²
Sylow	C₁₇₉ ⋊ C₂×D₈₁
Sylow	C₈₁ ⋊ C₂×D₁₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₁₄₄₉₉
commutator, cosocle, hypocenter	C₈₁×C₁₇₉	C₂²
Frattini	C₂₇	C₂×D₅₃₇
Fitting	C₂×C₈₁×C₁₇₉	C₂
socle	C₂×C₃×C₁₇₉	D₂₇
LCS	G ▷ C₈₁×C₁₇₉
UCS	C₁ ◁ C₂

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 262
transitive degree	μ_t(G) = 28998

A minimal faithful permutation representation — 2 generators on 262 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83)(84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262);(4,83)(5,82)(6,81)(7,80)(8,79)(9,78)(10,77)(11,76)(12,75)(13,74)(14,73)(15,72)(16,71)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,61)(27,60)(28,59)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(85,262)(86,261)(87,260)(88,259)(89,258)(90,257)(91,256)(92,255)(93,254)(94,253)(95,252)(96,251)(97,250)(98,249)(99,248)(100,247)(101,246)(102,245)(103,244)(104,243)(105,242)(106,241)(107,240)(108,239)(109,238)(110,237)(111,236)(112,235)(113,234)(114,233)(115,232)(116,231)(117,230)(118,229)(119,228)(120,227)(121,226)(122,225)(123,224)(124,223)(125,222)(126,221)(127,220)(128,219)(129,218)(130,217)(131,216)(132,215)(133,214)(134,213)(135,212)(136,211)(137,210)(138,209)(139,208)(140,207)(141,206)(142,205)(143,204)(144,203)(145,202)(146,201)(147,200)(148,199)(149,198)(150,197)(151,196)(152,195)(153,194)(154,193)(155,192)(156,191)(157,190)(158,189)(159,188)(160,187)(161,186)(162,185)(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)

Conjugacy classes & character table

14502 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83)(84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262), (4,83)(5,82)(6,81)(7,80)(8,79)(9,78)(10,77)(11,76)(12,75)(13,74)(14,73)(15,72)(16,71)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,61)(27,60)(28,59)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(85,262)(86,261)(87,260)(88,259)(89,258)(90,257)(91,256)(92,255)(93,254)(94,253)(95,252)(96,251)(97,250)(98,249)(99,248)(100,247)(101,246)(102,245)(103,244)(104,243)(105,242)(106,241)(107,240)(108,239)(109,238)(110,237)(111,236)(112,235)(113,234)(114,233)(115,232)(116,231)(117,230)(118,229)(119,228)(120,227)(121,226)(122,225)(123,224)(124,223)(125,222)(126,221)(127,220)(128,219)(129,218)(130,217)(131,216)(132,215)(133,214)(134,213)(135,212)(136,211)(137,210)(138,209)(139,208)(140,207)(141,206)(142,205)(143,204)(144,203)(145,202)(146,201)(147,200)(148,199)(149,198)(150,197)(151,196)(152,195)(153,194)(154,193)(155,192)(156,191)(157,190)(158,189)(159,188)(160,187)(161,186)(162,185)(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174));

C2×D14499 #72292592