C₅×#226⋊C₈ #14510732

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×#226⋊C₈
unambiguous semidirect product	#226⋊(C₅×C₈)

196 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5)(6,7,8,10,9,11,12,13)(14,24,26)(15,20,29,19,25,28)(16,23,18)(21,22);(14,15,18,19)(16,22,24,21)(17,25,27,20)(23,29,26,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236430);