C₃₇×#2253 #17991071

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#2253

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 77 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)(46,47,49,52)(48,56,58,70)(50,63,61,76)(51,64,62,55)(53,67,65,59)(54,69,66,57)(60,75,74,72)(68,73,71,77);(38,40,41,45)(39,42,43,44)(47,52)(53,65)(54,66)(55,64)(56,70)(63,76)(68,71)(72,75);(46,48,57,73,51,60,61,67,49,58,69,77,62,74,50,59)(47,53,63,72,55,68,66,70,52,65,76,75,64,71,54,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7452, C₃₇×#7454, C₃₇×#12463, …
maximal normal subgroup of	C₃₇×#7452, C₃₇×#7454, C₃₇×#12463, …
maximal quotient of	C₃₇×#12907, C₃₇×#13165, C₃₇×#13166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 985);

C37×#2253 #17991071