M₁₆×C₂²⋊H(3,𝔽₃) #13152216

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	M₁₆×C₂²⋊H(3,𝔽₃)
unambiguous semidirect product	(C₂²×M₁₆)⋊H(3,𝔽₃)
unambiguous semidirect product	(C₃²×M₁₆)⋊A₄
unambiguous semidirect product	(C₃×A₄×M₁₆)⋊C₃

Fitting	C₂²×C₃²×M₁₆ ⋊ C₃
Sylow	C₂²×M₁₆ ⋊ H(3,𝔽₃)

478 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18279);