C₅×C₃⋊(A₄⋊C₈) #13086213

order	1440
isoclinism	isoclinic class of C₃⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₅×C₃⋊(A₄⋊C₈)
unambiguous semidirect product	C₃⋊(C₅×A₄⋊C₈)
unambiguous semidirect product	A₄⋊(C₅×C₃⋊C₈)

C₃×A₄ ⋊ C₅×C₈

136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 360

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2530);