C₃₇×#2398 #17991216

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2398

Subgroups

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

568 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)(42,43,46,48)(44,49,45,47)(50,51,53,55)(52,56,57,54);(38,39)(40,41)(42,44,46,45)(43,47,48,49)(50,52,53,57)(51,54,55,56);(39,41)(51,55)(54,56);(42,45,46,44)(43,47,48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9029, C₃₇×#9032, C₃₇×#10013, …
maximal normal subgroup of	C₃₇×#9029, C₃₇×#9032, C₃₇×#10013, …
maximal quotient of	C₃₇×#13842, C₃₇×#13847, C₃₇×#13850, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1130);

C37×#2398 #17991216