C₅×(C₂×S₄)⋊C₈ #14510836

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₅×(C₂×S₄)⋊C₈
unambiguous semidirect product	(C₂×S₄)⋊(C₅×C₈)

C₂³×C₅×C₈ ⋊ D₃

434 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 240

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236534);