C₃₇×#3567 #17992385

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

Aliases

direct product

C₃₇×#3567

Subgroups

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

950 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)(39,43)(40,46)(45,50)(47,52)(54,55)(56,59)(57,62)(58,63)(60,64)(61,66)(65,67)(68,69);(39,43)(44,49)(45,50)(51,53)(55,56)(57,64)(61,63)(65,69);(38,39)(40,44)(41,45)(42,43)(46,49)(47,51)(48,50)(52,53)(54,56,59,55)(57,62,64,60)(58,63,66,61)(65,68,69,67);(38,40,42,46)(39,44,43,49)(41,47,48,52)(45,51,50,53)(54,57)(55,60)(56,62)(58,65)(59,64)(61,67)(63,68)(66,69);(38,41,42,48)(39,45,43,50)(40,47,46,52)(44,51,49,53)(54,58)(55,61)(56,63)(57,65)(59,66)(60,67)(62,68)(64,69)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8515, C₃₇×#19040, C₃₇×#19041, …
maximal normal subgroup of	C₃₇×#8515, C₃₇×#19040, C₃₇×#19041, …
maximal quotient of	C₃₇×#34405, C₃₇×#34449, C₃₇×#34450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2299);

C37×#3567 #17992385