C₃₇×#3268 #17992086

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3268

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×D₄×C₃₇ ◁ G

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 57 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)(43,47)(45,53)(48,54)(49,50)(51,57)(55,56);(42,43,46,50)(44,48,52,56)(45,49,53,47)(51,55,57,54);(39,41)(42,44,46,52)(43,48,50,56)(45,51,53,57)(47,54,49,55);(43,49)(45,53)(47,50)(48,55)(51,57)(54,56)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#3268, C₃₇×#61030, C₃₇×#61052, …
maximal normal subgroup of	C₂×C₃₇×#3268, C₃₇×#61030, C₃₇×#61052, …
maximal quotient of	C₃₇×#19759, C₃₇×#19767, C₃₇×#19777, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2000);

C37×#3268 #17992086