C₃₇×#2396 #17991214

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2396

Subgroups

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

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

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)(42,43)(44,47)(45,46)(48,49)(50,51,53,55)(52,56,57,54);(38,39)(40,41)(43,46)(47,49);(39,41)(50,52,53,57)(51,54,55,56);(42,44,45,48)(43,47,46,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9033, C₃₇×#9034, C₃₇×#11715, …
maximal normal subgroup of	C₃₇×#9033, C₃₇×#9034, C₃₇×#11715, …
maximal quotient of	C₃₇×#13844, C₃₇×#13846, C₃₇×#13848, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1128);

C37×#2396 #17991214