C₃₇×#2596 #17991414

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2596

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

398 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)(46,47,50,51)(48,53,52,49)(56,60)(59,61);(40,45)(43,44)(47,51)(48,52)(54,55,58,57)(56,59,60,61);(38,40,42,45)(39,43,41,44)(46,48,50,52)(47,49,51,53)(54,56)(55,59)(57,61)(58,60);(38,41,42,39)(40,44,45,43)(46,49)(47,52)(48,51)(50,53)(54,57,58,55)(56,61,60,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2596, C₃₇×#34856, C₃₇×#34866, …
maximal normal subgroup of	C₂×C₃₇×#2596, C₃₇×#34856, C₃₇×#34866, …
maximal quotient of	C₃₇×#13934, C₃₇×#13950, C₃₇×#14035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1328);

C37×#2596 #17991414