C₃₇×#2252 #17991070

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2252

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

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7450, C₃₇×#7451, C₃₇×#12392, …
maximal normal subgroup of	C₃₇×#7450, C₃₇×#7451, C₃₇×#12392, …
maximal quotient of	C₃₇×#12905, C₃₇×#13165, C₃₇×#13282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 984);

C37×#2252 #17991070