C₃₇×#2597 #17991415

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

Aliases

direct product

C₃₇×#2597

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

454 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)(40,42)(41,44)(43,45)(46,47,50,49)(48,52,53,51)(55,57)(59,60);(39,40)(43,44)(48,53)(51,52)(54,55,58,57)(56,60,61,59);(38,40,42,39)(41,44,45,43)(46,48,50,53)(47,51,49,52)(54,56,58,61)(55,59,57,60);(38,41)(39,43)(40,44)(42,45)(46,49,50,47)(48,52,53,51)(54,57,58,55)(56,60,61,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2597, C₃₇×#34856, C₃₇×#34861, …
maximal normal subgroup of	C₂×C₃₇×#2597, C₃₇×#34856, C₃₇×#34861, …
maximal quotient of	C₃₇×#13934, C₃₇×#13947, C₃₇×#14036, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1329);

C37×#2597 #17991415