C₃₇×#3565 #17992383

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3565

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#62159, C₃₇×#62160, C₃₇×#62161, …
maximal normal subgroup of	C₃₇×#62159, C₃₇×#62160, C₃₇×#62161, …
maximal quotient of	C₃₇×#34385, C₃₇×#34392, C₃₇×#34403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2297);

C37×#3565 #17992383