C₃₇×#2689 #17991507

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2689

Subgroups

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

456 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)(52,55)(53,57)(54,56);(39,41)(42,44,46,45)(43,47,48,49)(50,52,54,57)(51,55,56,53);(38,39)(40,41)(42,45,46,44)(43,47,48,49)(50,52)(51,53)(54,57)(55,56);(42,43)(44,49)(45,47)(46,48)(50,53)(51,52)(54,55)(56,57)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#36705, C₃₇×#36712, C₃₇×#36732, …
maximal normal subgroup of	C₃₇×#36705, C₃₇×#36712, C₃₇×#36732, …
maximal quotient of	C₃₇×#14364, C₃₇×#14368, C₃₇×#14381, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1421);

C37×#2689 #17991507