C₉×A₄×C₄⋊C₄ #13152106

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₉ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₉×A₄×C₄⋊C₄
unambiguous semidirect product	C₄⋊(C₄×C₉×A₄)

Fitting	C₂²×C₉×C₄⋊C₄ ⋊ C₃
Sylow	C₂²×C₄⋊C₄ ⋊ C₃×C₉

443 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

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

μ_t(G) = 432

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18169);