C₅×D₄×C₂²⋊C₉ #13085306

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×D₄×C₂²⋊C₉
unambiguous semidirect product	C₄⋊(C₂×C₅×C₂²⋊C₉)
unambiguous semidirect product	(C₂²×D₄)⋊(C₅×C₉)
unambiguous semidirect product	(C₂²×C₅×D₄)⋊C₉

Hall	C₂²×C₅×D₄ ⋊ C₉
Sylow	C₂²×D₄ ⋊ C₅×C₉

232 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 180

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1623);