C₃₇×#3191 #17992009

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3191

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12104, C₃₇×#12107, C₃₇×#12280, …
maximal normal subgroup of	C₃₇×#12104, C₃₇×#12107, C₃₇×#12280, …
maximal quotient of	C₃₇×#21760, C₃₇×#21939, C₃₇×#22042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1923);

C37×#3191 #17992009