C₃₇×#2809 #17991627

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#2809

Subgroups

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

368 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7743, C₃₇×#7760, C₃₇×#7771, …
maximal normal subgroup of	C₃₇×#7743, C₃₇×#7760, C₃₇×#7771, …
maximal quotient of	C₃₇×#14446, C₃₇×#14464, C₃₇×#14467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1541);