C₃₇×#2956 #17991774

order	4736
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2956

Subgroups

	subgroup	G/H
center	C₄×C₃₇	C₂²×D₄
commutator	C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂×C₃₇	C₂×C₄×D₄
prime radical	C₃₇×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂×M₁₆×C₃₇ ◁ G

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

A minimal faithful permutation representation — 4 generators on 53 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)(38,39,42,46,43,40,47,45)(41,44,50,52,49,48,53,51);(38,40)(39,43)(41,48)(42,45)(44,49)(46,47)(50,51)(52,53);(38,41,42,50,43,49,47,53)(39,44,46,52,40,48,45,51);(41,49)(44,48)(50,53)(51,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#11669, C₃₇×#11670, C₃₇×#22898, …
maximal normal subgroup of	C₃₇×#11669, C₃₇×#11670, C₃₇×#22898, …
maximal quotient of	C₃₇×#17852, C₃₇×#17853, C₃₇×#17873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1688);

C37×#2956 #17991774