C₃₇×#3111 #17991929

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3111

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

392 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)(48,56)(49,54)(50,55)(51,53)(52,58)(57,60)(59,61);(39,42)(43,45)(46,48,50,58)(47,52,55,56)(49,57,51,59)(53,60,54,61);(47,53)(49,51)(52,60)(54,55)(56,61)(57,59);(38,40,41,44)(39,43,42,45)(46,49,50,51)(47,54,55,53)(48,57,58,59)(52,61,56,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#3111, C₃₇×#60546, C₃₇×#60559, …
maximal normal subgroup of	C₂×C₃₇×#3111, C₃₇×#60546, C₃₇×#60559, …
maximal quotient of	C₃₇×#20742, C₃₇×#21121, C₃₇×#21122, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1843);

C37×#3111 #17991929