C₃₇×#2674 #17991492

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2674

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

562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 53 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)(39,41)(46,47,50,52)(48,53,49,51);(43,45)(46,48,50,49)(47,51,52,53);(38,39)(40,41)(42,43)(44,45)(46,49,50,48)(47,51,52,53);(38,39)(40,41)(46,47)(48,53)(49,51)(50,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36705, C₃₇×#36711, C₃₇×#36712, …
maximal normal subgroup of	C₃₇×#36705, C₃₇×#36711, C₃₇×#36712, …
maximal quotient of	C₃₇×#14360, C₃₇×#14364, C₃₇×#14382, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1406);

C37×#2674 #17991492