C₃₇×#3137 #17991955

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#3137

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

372 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)(46,47,51,53)(48,54,55,61)(49,50,57,58)(52,59,60,56);(39,42)(43,45)(46,48,50,56,51,55,58,59)(47,52,49,54,53,60,57,61);(38,40,41,44)(39,43,42,45)(46,49,50,53,51,57,58,47)(48,54,56,60,55,61,59,52);(48,55)(52,60)(54,61)(56,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#26849, C₃₇×#26851, C₃₇×#26852, …
maximal normal subgroup of	C₃₇×#26849, C₃₇×#26851, C₃₇×#26852, …
maximal quotient of	C₃₇×#20763, C₃₇×#21087, C₃₇×#21088, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1869);

C37×#3137 #17991955