C₃×A₄×C₄⋊Q₈ #11919712

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

direct product	C₃×A₄×C₄⋊Q₈
unambiguous semidirect product	C₄⋊(C₃×Q₈×A₄)
unambiguous semidirect product	(C₂²×C₄⋊Q₈)⋊C₃²
unambiguous semidirect product	(C₂²×C₃×C₄⋊Q₈)⋊C₃

Fitting	C₂²×C₃×C₄⋊Q₈ ⋊ C₃
Sylow	C₂²×C₄⋊Q₈ ⋊ C₃²

904 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.

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

μ_t(G) = 288

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153723);