C₃₇×#3319 #17992137

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3319

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×D₄×C₃₇ ◁ G

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 61 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)(38,39,41,43)(40,44,45,42)(46,47,51,54)(48,52,50,59)(49,56,58,60)(53,57,61,55);(38,40)(39,42)(41,45)(43,44)(46,48,51,50)(47,52,54,59)(49,57,58,55)(53,56,61,60);(46,49)(47,53)(48,55)(50,57)(51,58)(52,60)(54,61)(56,59);(40,45)(42,44)(46,48,51,50)(47,52,54,59)(49,55,58,57)(53,60,61,56)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#3319, C₃₇×#61141, C₃₇×#61156, …
maximal normal subgroup of	C₂×C₃₇×#3319, C₃₇×#61141, C₃₇×#61156, …
maximal quotient of	C₃₇×#22424, C₃₇×#22492, C₃₇×#22564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2051);

C37×#3319 #17992137