C₃₇×#2642 #17991460

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2642

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

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

normal subgroups only

This group has 416 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) = 65
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 generators on 65 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)(38,39,40,41)(44,48)(46,49)(51,55)(56,58)(57,63)(64,65);(38,39,40,41)(42,43,45,47)(44,46,48,49)(50,51)(52,58)(53,57)(54,55)(56,60)(59,65)(61,64)(62,63);(38,39)(40,41)(42,44)(43,46)(45,48)(47,49)(50,52,54,60)(51,56,55,58)(53,61,62,59)(57,65,63,64);(50,53,54,62)(51,57,55,63)(52,59,60,61)(56,64,58,65)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#10095, C₃₇×#10103, C₃₇×#18441, …
maximal normal subgroup of	C₃₇×#10095, C₃₇×#10103, C₃₇×#18441, …
maximal quotient of	C₃₇×#14261, C₃₇×#14274, C₃₇×#14283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1374);