C₃₇×#1840 #17990658

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1840

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 69 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)(40,45)(41,43)(42,44)(46,47)(48,50)(49,51)(52,53)(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69);(38,40,42,41)(39,43,44,45)(46,48,49,52)(47,50,51,53)(54,56)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69);(38,41,42,40)(39,43,44,45)(47,51)(50,53)(56,62)(59,65)(63,68)(66,69)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#1840, C₃₇×#20773, C₃₇×#20774, …
maximal normal subgroup of	C₂×C₃₇×#1840, C₃₇×#20773, C₃₇×#20774, …
maximal quotient of	C₃₇×#8802, C₃₇×#10796, C₃₇×#11298, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 572);

C37×#1840 #17990658