C₃₇×#2960 #17991778

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2960

Subgroups

	subgroup	G/H
center	C₂×C₈×C₃₇	C₂³
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₇ ◁ G

364 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)(40,45)(41,43)(42,44)(46,47,49,53,50,52,56,59)(48,51,54,58,55,57,60,61);(38,40,42,41)(39,43,44,45);(38,41,42,40)(39,43,44,45)(46,48,49,54,50,55,56,60)(47,51,53,58,52,57,59,61);(47,52)(51,57)(53,59)(58,61)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8242, C₃₇×#8244, C₃₇×#8246, …
maximal normal subgroup of	C₃₇×#8242, C₃₇×#8244, C₃₇×#8246, …
maximal quotient of	C₃₇×#20435, C₃₇×#20437, C₃₇×#20516, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1692);

C37×#2960 #17991778