A₅×#11757162 #72228124

order	57600
isoclinism	isoclinic class of A₅×#11757162
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

Fitting	C₂⁴ ⋊ A₅²
socle	C₂⁴×A₅ ⋊ A₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂⁴	A₅²
socle	C₂⁴×A₅	A₅
LCS	G
UCS	C₁

1563 conjugacy classes of subgroups; only the 6 normal subgroups are shown.

normal subgroups only

This group has 1563 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

(1,12,16,7,8)(2,3,13,11,9)(4,14,6,5,10)(17,19,20,21,18);(2,6,13)(3,10,16)(4,12,5)(7,8,11)(9,14,15)(17,18)(19,20)

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

gap> G := Group((1,12,16,7,8)(2,3,13,11,9)(4,14,6,5,10)(17,19,20,21,18), (2,6,13)(3,10,16)(4,12,5)(7,8,11)(9,14,15)(17,18)(19,20));