C₅×C₄⋊#857 #14510706

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×C₄⋊#857
unambiguous semidirect product	C₄⋊(C₅×#857)

C₄³×C₅ ⋊ D₃

328 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236404);