C₃₇×#3290 #17992108

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3290

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂×C₄×C₃₇ ◁ G

454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 69 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)(40,49)(41,46)(42,59)(43,48)(44,52)(45,57)(47,60)(50,62)(51,68)(53,64)(54,63)(55,61)(56,66)(58,65)(67,69);(38,40)(39,44)(41,55)(42,53)(43,54)(45,62)(46,67)(47,63)(48,64)(49,59)(50,58)(51,56)(52,60)(57,69)(61,66)(65,68);(38,41)(39,45)(40,50)(42,56)(43,58)(44,61)(46,59)(47,65)(48,66)(49,68)(51,52)(53,69)(54,55)(57,60)(62,64)(63,67);(38,41)(39,46)(40,51)(42,57)(43,58)(44,62)(45,59)(47,66)(48,65)(49,68)(50,52)(53,55)(54,69)(56,60)(61,64)(63,67)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#33854, C₃₇×#33855, C₃₇×#33857, …
maximal normal subgroup of	C₃₇×#33854, C₃₇×#33855, C₃₇×#33857, …
maximal quotient of	C₃₇×#19883, C₃₇×#19886, C₃₇×#19889, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2022);

C37×#3290 #17992108