C₃₇×#2730 #17991548

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2730

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₃₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

548 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)(42,43,46,44)(45,48,49,47)(50,51)(52,54)(53,55)(56,57);(39,41)(43,44)(45,49)(51,52)(53,57);(38,39)(40,41)(42,44,46,43)(45,48,49,47)(50,52,54,51)(53,56,57,55);(42,45,46,49)(43,47,44,48)(50,53)(51,55)(52,56)(54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36758, C₃₇×#36766, C₃₇×#36767, …
maximal normal subgroup of	C₃₇×#36758, C₃₇×#36766, C₃₇×#36767, …
maximal quotient of	C₃₇×#14393, C₃₇×#14397, C₃₇×#14400, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1462);

C37×#2730 #17991548