Q₁₆×C₂²⋊H(3,𝔽₃) #13152231

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	Q₁₆×C₂²⋊H(3,𝔽₃)
unambiguous semidirect product	(C₂²×Q₁₆)⋊H(3,𝔽₃)
unambiguous semidirect product	(C₃²×Q₁₆)⋊A₄
unambiguous semidirect product	(C₃×A₄×Q₁₆)⋊C₃

Fitting	C₂²×C₃²×Q₁₆ ⋊ C₃
Sylow	C₂²×Q₁₆ ⋊ H(3,𝔽₃)

420 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18294);