C₃₇×#3099 #17991917

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3099

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(38,39)(40,43)(41,42)(44,45)(46,47,51,55)(48,52,57,61)(49,54,50,59)(53,58,60,56);(39,42)(43,45)(46,48)(47,52)(49,58)(50,56)(51,57)(53,59)(54,60)(55,61);(38,40,41,44)(39,43,42,45)(46,48)(47,53)(49,56)(50,58)(51,57)(52,59)(54,61)(55,60);(46,49,51,50)(47,54,55,59)(48,56,57,58)(52,53,61,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#24926, C₃₇×#24927, C₃₇×#24929, …
maximal normal subgroup of	C₃₇×#24926, C₃₇×#24927, C₃₇×#24929, …
maximal quotient of	C₃₇×#20703, C₃₇×#20848, C₃₇×#20915, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1831);

C37×#3099 #17991917