C₃₇×#3584 #17992402

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

Aliases

direct product

C₃₇×#3584

Subgroups

	subgroup	G/H
center	C₄×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₇
socle	C₂×C₃₇	C₂³×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

1424 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)(40,49)(41,46)(42,47)(43,56)(44,48)(45,51)(50,63)(52,59)(53,61)(54,62)(55,66)(57,60)(58,65)(64,69)(67,68);(38,40)(39,45)(41,50)(42,51)(43,57)(44,52)(46,58)(47,59)(48,60)(49,56)(53,64)(54,65)(55,67)(61,68)(62,69)(63,66);(38,41)(39,46)(40,50)(42,54)(43,55)(44,53)(45,58)(47,62)(48,61)(49,63)(51,65)(52,64)(56,66)(57,67)(59,69)(60,68);(41,53)(46,61)(50,64)(54,55)(58,68)(62,66)(63,69)(65,67);(38,42,44,43)(39,47,48,56)(40,51,52,57)(41,54,53,55)(45,59,60,49)(46,62,61,66)(50,65,64,67)(58,69,68,63)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12745, C₃₇×#12746, C₃₇×#12747, …
maximal normal subgroup of	C₃₇×#12745, C₃₇×#12746, C₃₇×#12747, …
maximal quotient of	C₃₇×#60086, C₃₇×#60108, C₃₇×#60161, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2316);

C37×#3584 #17992402