C₃₇×#3512 #17992330

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3512

Subgroups

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

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 5 generators on 61 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)(40,44)(42,45)(46,47)(48,53)(49,54)(50,58)(51,52)(55,59)(56,57)(60,61);(38,39,41,43)(40,42,44,45)(47,52)(49,53)(55,58)(57,60);(38,40,41,44)(39,42,43,45)(46,48,51,54)(47,53,52,49)(50,56,59,61)(55,60,58,57);(46,49,51,53)(47,54,52,48)(50,57,59,60)(55,61,58,56);(46,50,51,59)(47,55,52,58)(48,56,54,61)(49,57,53,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8476, C₃₇×#17687, C₃₇×#17690, …
maximal normal subgroup of	C₃₇×#8476, C₃₇×#17687, C₃₇×#17690, …
maximal quotient of	C₃₇×#34189, C₃₇×#34208, C₃₇×#34217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2244);

C37×#3512 #17992330