C₃×D₃₈₅₉ #37529166

order	23154
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃₈₅₉
unambiguous semidirect product	C₁₇⋊(C₃×D₂₂₇)
unambiguous semidirect product	C₂₂₇⋊(C₃×D₁₇)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₂₂₇ ⋊ C₂
derived, Hall	C₁₇×C₂₂₇ ⋊ C₂×C₃
Hall	C₃×C₂₂₇ ⋊ D₁₇
Sylow	C₂₂₇ ⋊ C₃×D₁₇
Hall	C₃×C₁₇ ⋊ D₂₂₇
Sylow	C₁₇ ⋊ C₃×D₂₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃₈₅₉
commutator, cosocle, hypocenter	C₁₇×C₂₂₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₂₂₇	C₂
LCS	G ▷ C₁₇×C₂₂₇
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 247
transitive degree	μ_t(G) = 11577

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

Conjugacy classes & character table

5793 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23154, 4);

C3×D3859 #37529166