#72240874

order	3840
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, prime radical, cosocle, hypocenter	#14515303	C₂
Frattini, Fitting	C₂⁵	S₅
socle	C₂⁴	#6728
LCS	G ▷ #14515303
UCS	C₁

107 conjugacy classes of subgroups; only the 5 normal subgroups are shown.

normal subgroups only

This group has 107 conjugacy classes of subgroups — too many to draw. Only its 5 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) = 40
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 40 points:

(1,37,23,17,14,2,18,35,5,11)(3,25,15,12,4,7,31,29,9,8)(6,39,30,28,32,20,21,16,22,26)(10,27,36,40,19,13,33,24,34,38);(1,9,7,5,3,17,2,12)(4,36,13,40,14,24,20,28)(6,34,8,30,10,22,11,16)(15,37,33,26,35,18,39,19)(21,38,23,31,27,32,29,25)

Conjugacy classes & character table

19 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72240876
maximal normal subgroup of	#72240876

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,37,23,17,14,2,18,35,5,11)(3,25,15,12,4,7,31,29,9,8)(6,39,30,28,32,20,21,16,22,26)(10,27,36,40,19,13,33,24,34,38), (1,9,7,5,3,17,2,12)(4,36,13,40,14,24,20,28)(6,34,8,30,10,22,11,16)(15,37,33,26,35,18,39,19)(21,38,23,31,27,32,29,25));