C₃₇×#2166 #17990984

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#2166

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#117
commutator	C₂×C₄	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
socle	C₂×C₃₇	#432
prime radical	C₂³×C₃₇	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ #97×C₃₇ ◁ G

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(38,39,41,47,42,48,55,64,43,46,54,62,56,45,59,61)(40,49,51,63,52,60,66,69,50,44,53,58,65,57,67,68);(38,40)(39,44)(41,53)(42,52)(43,50)(45,60)(46,49)(47,63)(48,57)(51,54)(55,67)(56,65)(58,62)(59,66)(61,68)(64,69);(39,45,46,48)(40,50)(41,54)(44,57,49,60)(47,64,62,61)(52,65)(55,59)(58,69,63,68)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7239, C₃₇×#7240, C₃₇×#11537, …
maximal normal subgroup of	C₃₇×#7239, C₃₇×#7240, C₃₇×#11537, …
maximal quotient of	C₃₇×#12596, C₃₇×#12608, C₃₇×#12660, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 898);

C37×#2166 #17990984