C₃₇×#2776 #17991594

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

Aliases

direct product

C₃₇×#2776

Subgroups

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

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36762, C₃₇×#36768, C₃₇×#36782, …
maximal normal subgroup of	C₃₇×#36762, C₃₇×#36768, C₃₇×#36782, …
maximal quotient of	C₃₇×#14387, C₃₇×#14390, C₃₇×#14435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1508);

C37×#2776 #17991594