C₃₇×#2658 #17991476

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₇×#2658

Subgroups

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

612 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)(38,39,40,41)(47,51)(48,54)(53,59)(56,57);(42,43,44,45)(46,47)(48,55)(49,53)(50,51)(52,54)(56,61)(57,60)(58,59);(38,39)(40,41)(42,43)(44,45)(46,48)(47,52)(49,57)(50,54)(51,55)(53,61)(56,58)(59,60);(46,49,50,58)(47,53,51,59)(48,56,54,57)(52,60,55,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#10094, C₃₇×#10102, C₃₇×#18437, …
maximal normal subgroup of	C₃₇×#10094, C₃₇×#10102, C₃₇×#18437, …
maximal quotient of	C₃₇×#14273, C₃₇×#14274, C₃₇×#14322, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1390);

C37×#2658 #17991476