C₃₇×#3322 #17992140

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3322

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 ◁ C₄×D₄×C₃₇ ◁ G

414 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)(38,39,41,43)(40,44,45,42)(46,47)(48,51)(49,52)(50,53)(54,57)(55,59)(56,60)(58,61);(38,40)(39,42)(41,45)(43,44)(46,48)(47,51)(49,56)(50,55)(52,60)(53,59)(54,58)(57,61);(47,52)(48,55)(49,57)(51,58)(53,54)(59,60);(40,45)(42,44)(47,53)(51,59)(52,54)(58,60)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#3322, C₃₇×#61154, C₃₇×#61156, …
maximal normal subgroup of	C₂×C₃₇×#3322, C₃₇×#61154, C₃₇×#61156, …
maximal quotient of	C₃₇×#22427, C₃₇×#22501, C₃₇×#22578, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2054);

C37×#3322 #17992140