C₃₇×#2401 #17991219

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2401

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
socle	C₂³×C₃₇	C₂⁴
prime radical	C₂⁴×C₃₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 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)(40,43)(41,42)(44,45)(46,47,49,51)(48,50,52,53)(54,55,57,59)(56,58,60,61);(39,42)(43,45)(46,48,49,52)(47,50,51,53)(54,56)(55,58)(57,60)(59,61);(47,51)(50,53)(56,60)(58,61);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#21668, C₃₇×#21669, C₃₇×#21670, …
maximal normal subgroup of	C₃₇×#21668, C₃₇×#21669, C₃₇×#21670, …
maximal quotient of	C₃₇×#13842, C₃₇×#13846, C₃₇×#13855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1133);