C₃₇×#1747 #17990565

order	4736
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₃₇×#1747

Subgroups

	subgroup	G/H
center	C₈×C₃₇	C₄²
commutator	C₄	C₂×C₄²×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle	C₂×C₃₇	#376
prime radical	C₂³×C₃₇	#41
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ G

200 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)(40,48,51,61)(41,45)(42,46)(43,47)(44,50,56,64)(49,60,63,68)(52,57)(53,58)(54,59)(55,62,66,69)(65,67);(38,40)(39,44,47,56)(41,49)(42,50)(43,51)(45,55,58,66)(46,48,59,61)(52,62)(53,63)(54,64)(57,60,67,68)(65,69);(38,41,42,52,43,53,54,65)(39,45,46,57,47,58,59,67)(40,49,50,62,51,63,64,69)(44,55,48,60,56,66,61,68)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#11769, C₃₇×#11770, C₃₇×#11771, …
maximal normal subgroup of	C₃₇×#11769, C₃₇×#11770, C₃₇×#11771, …
maximal quotient of	C₃₇×#8137, C₃₇×#8138, C₃₇×#8139, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 479);

C37×#1747 #17990565