C₂×D₁₅₄₇₁ #72297601

order	61884
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₃₀₉₄₂
direct product	C₂×D₁₅₄₇₁

Splittings

Fitting	C₂×C₈₁×C₁₉₁ ⋊ C₂
derived, Hall	C₈₁×C₁₉₁ ⋊ C₂²
Sylow	C₁₉₁ ⋊ C₂×D₈₁
Sylow	C₈₁ ⋊ C₂×D₁₉₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₁₅₄₇₁
commutator, cosocle, hypocenter	C₈₁×C₁₉₁	C₂²
Frattini	C₂₇	C₂×D₅₇₃
Fitting	C₂×C₈₁×C₁₉₁	C₂
socle	C₂×C₃×C₁₉₁	D₂₇
LCS	G ▷ C₈₁×C₁₉₁
UCS	C₁ ◁ C₂

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 274
transitive degree	μ_t(G) = 30942

A minimal faithful permutation representation — 2 generators on 274 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)(84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274);(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)(85,274)(86,273)(87,272)(88,271)(89,270)(90,269)(91,268)(92,267)(93,266)(94,265)(95,264)(96,263)(97,262)(98,261)(99,260)(100,259)(101,258)(102,257)(103,256)(104,255)(105,254)(106,253)(107,252)(108,251)(109,250)(110,249)(111,248)(112,247)(113,246)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,239)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,232)(128,231)(129,230)(130,229)(131,228)(132,227)(133,226)(134,225)(135,224)(136,223)(137,222)(138,221)(139,220)(140,219)(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,204)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,197)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,190)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)

Conjugacy classes & character table

15474 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)(84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274), (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)(85,274)(86,273)(87,272)(88,271)(89,270)(90,269)(91,268)(92,267)(93,266)(94,265)(95,264)(96,263)(97,262)(98,261)(99,260)(100,259)(101,258)(102,257)(103,256)(104,255)(105,254)(106,253)(107,252)(108,251)(109,250)(110,249)(111,248)(112,247)(113,246)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,239)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,232)(128,231)(129,230)(130,229)(131,228)(132,227)(133,226)(134,225)(135,224)(136,223)(137,222)(138,221)(139,220)(140,219)(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,204)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,197)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,190)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180));

C2×D15471 #72297601