C₃₇×#2843 #17991661

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2843

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

348 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 184 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)(38,39,41,43)(40,42,44,45)(46,47)(48,52)(49,53)(50,51);(40,44)(42,45)(47,51)(49,52)(54,55,57,59)(56,60,61,58);(38,39)(40,42)(41,43)(44,45)(46,48)(47,52)(49,51)(50,53)(54,56,57,61)(55,58,59,60);(38,40)(39,42)(41,44)(43,45)(46,49,50,52)(47,53,51,48)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#12183, C₃₇×#12259, C₂×C₃₇×#2843, …
maximal normal subgroup of	C₃₇×#12183, C₃₇×#12259, C₂×C₃₇×#2843, …
maximal quotient of	C₃₇×#14638, C₃₇×#14639, C₃₇×#14640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1575);