C₃₇×#2742 #17991560

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2742

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂⁴×C₃₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12178, C₃₇×#12254, C₃₇×#36729, …
maximal normal subgroup of	C₃₇×#12178, C₃₇×#12254, C₃₇×#36729, …
maximal quotient of	C₃₇×#14370, C₃₇×#14402, C₃₇×#14459, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1474);

C37×#2742 #17991560