C₅×Q₈⋊#168 #13099447

order	1600
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×Q₈⋊#168
unambiguous semidirect product	Q₈⋊(C₅×#168)

C₅² ⋊ Q₈⋊C₈

210 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

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

μ_t(G) = 320

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1799);