C₃₇×#2654 #17991472

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2654

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

378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 61 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)(39,42)(43,45)(46,47,50,49)(48,52,53,51)(55,56)(59,60);(48,53)(51,52)(54,55,58,56)(57,59,61,60);(38,39)(40,43)(41,42)(44,45)(46,48)(47,51)(49,52)(50,53)(54,56,58,55)(57,59,61,60);(38,40,41,44)(39,43,42,45)(46,49,50,47)(48,52,53,51)(54,57,58,61)(55,59,56,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2654, C₃₇×#34584, C₃₇×#34592, …
maximal normal subgroup of	C₂×C₃₇×#2654, C₃₇×#34584, C₃₇×#34592, …
maximal quotient of	C₃₇×#14268, C₃₇×#14270, C₃₇×#14279, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1386);

C37×#2654 #17991472