C₃₇×#3586 #17992404

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₇×#3586

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

1412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 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)(40,48)(41,45)(42,54)(43,46)(44,50)(47,56)(49,62)(51,61)(52,59)(53,66)(55,58)(57,64)(60,65)(63,69)(67,68);(38,40,43,51)(39,44,46,58)(41,49,52,63)(42,55,56,50)(45,57,59,68)(47,61,54,48)(53,67,65,64)(60,69,66,62);(38,41)(39,45)(40,49)(42,53)(43,52)(44,57)(46,59)(47,60)(48,62)(50,64)(51,63)(54,66)(55,67)(56,65)(58,68)(61,69);(41,52)(45,59)(49,63)(53,65)(57,68)(60,66)(62,69)(64,67);(39,46)(44,58)(45,59)(47,54)(48,61)(57,68)(60,66)(62,69)

Conjugacy classes & character table

1517 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#23873, C₃₇×#23875, C₃₇×#23884, …
maximal normal subgroup of	C₃₇×#23873, C₃₇×#23875, C₃₇×#23884, …
maximal quotient of	C₃₇×#60088, C₃₇×#60089, C₃₇×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2318);

C37×#3586 #17992404