C₂×C₃⋊C₈×C₂²⋊C₉ #13147256

order	1728
isoclinism	isoclinic class of D₃×A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₃⋊C₈×C₂²⋊C₉
unambiguous semidirect product	(C₂×C₃)⋊(C₈×C₂²⋊C₉)
unambiguous semidirect product	(C₂³×C₃⋊C₈)⋊C₉

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

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

μ_t(G) = 144

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 13319);