C₃₇×#2681 #17991499

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

Aliases

direct product

C₃₇×#2681

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂×#121×C₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

618 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)(38,39,40,41)(46,47)(48,53)(49,50)(51,52);(43,45)(46,48,51,49)(47,50,52,53);(38,39)(40,41)(42,43)(44,45)(46,49,51,48)(47,50,52,53);(38,39)(40,41)(46,50)(47,48)(49,52)(51,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36716, C₃₇×#36718, C₃₇×#36719, …
maximal normal subgroup of	C₃₇×#36716, C₃₇×#36718, C₃₇×#36719, …
maximal quotient of	C₃₇×#14360, C₃₇×#14361, C₃₇×#14362, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1413);

C37×#2681 #17991499