C₃₇×#3500 #17992318

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₇×#3500

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(39,41)(42,43)(44,50)(45,53)(46,47)(48,52)(49,54)(51,55)(56,57);(43,47)(48,50)(49,53)(55,56);(38,39,40,41)(42,44)(43,48)(45,51)(46,52)(47,50)(49,55)(53,56)(54,57);(42,43)(44,48)(45,49)(46,47)(50,52)(51,55)(53,54)(56,57);(42,45,46,54)(43,49,47,53)(44,51,52,57)(48,55,50,56)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8475, C₃₇×#12715, C₃₇×#12716, …
maximal normal subgroup of	C₃₇×#8475, C₃₇×#12715, C₃₇×#12716, …
maximal quotient of	C₃₇×#34184, C₃₇×#34208, C₃₇×#34211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2232);

C37×#3500 #17992318