C₃₇×#1832 #17990650

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1832

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7065, C₃₇×#8877, C₃₇×#10513, …
maximal normal subgroup of	C₃₇×#7065, C₃₇×#8877, C₃₇×#10513, …
maximal quotient of	C₃₇×#8782, C₃₇×#8783, C₃₇×#8787, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 564);

C37×#1832 #17990650