C₃₇×C₁₈₁⋊C₃ #34095609

order	20091
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₇×C₁₈₁⋊C₃
unambiguous semidirect product	C₁₈₁⋊(C₃×C₃₇)

Splittings

Fitting, socle, Hall	C₃₇×C₁₈₁ ⋊ C₃
derived, Sylow	C₁₈₁ ⋊ C₃×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	C₁₈₁⋊C₃
commutator, cosocle, hypocenter	C₁₈₁	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃₇×C₁₈₁	C₃
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₃₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 218
transitive degree	μ_t(G) = 6697

A minimal faithful permutation representation — 2 generators on 218 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,116)(76,97,113)(79,95,110)(82,102,107)(85,105,104)(88,108,101)(91,111,99)(93,114,96)(98,119,137)(100,120,134)(103,124,131)(106,126,128)(109,129,125)(112,132,123)(115,135,121)(117,138,118)(122,141,153)(127,144,148)(130,146,145)(133,149,143)(136,151,142)(139,154,140)(147,159,160)(150,161,158)(152,163,157)(155,165,156)(162,170,169)(164,171,168)(166,173,167)(172,177,176)(174,178,175)(179,181,180)(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);(1,2,4,8,15,25,38,54,73,95,56,24,36,50,66,85,106,127,138,92,113,134,94,117,139,155,166,174,179,178,163,132,87,49,22,32,45,61,80,101,123,142,156,159,126,81,43,17,3,6,11,18,28,41,57,76,98,120,75,37,52,69,88,109,130,147,154,114,70,89,110,131,148,160,169,176,180,181,171,149,108,65,33,12,19,29,42,58,77,99,121,140,144,102,59,27,7,13,21,31,44,60,79,100,122,141,97,53,71,91,112,133,150,162,165,135,90,51,67,86,107,128,145,158,168,175,177,161,129,84,46,20,5,9,16,26,39,55,74,96,118,124,78,40,14,23,34,47,63,82,103,116,137,153,119,72,93,115,136,152,164,172,173,151,111,68,35,48,64,83,104,125,143,157,167,170,146,105,62,30,10)

Conjugacy classes & character table

2331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20091, 2);

C37×C181⋊C3 #34095609