C₃₇×#2722 #17991540

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

Aliases

direct product

C₃₇×#2722

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

448 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)(44,45)(46,47)(48,49)(50,51)(52,57)(53,56)(54,55);(39,41)(43,47)(45,48)(50,52,55,53)(51,56,54,57);(38,39)(40,41)(42,44)(43,48)(45,47)(46,49)(50,53,55,52)(51,56,54,57);(42,45,46,48)(43,44,47,49)(50,54,55,51)(52,56,53,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12150, C₃₇×#12244, C₃₇×#36728, …
maximal normal subgroup of	C₃₇×#12150, C₃₇×#12244, C₃₇×#36728, …
maximal quotient of	C₃₇×#14369, C₃₇×#14388, C₃₇×#14395, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1454);

C37×#2722 #17991540