C₂×C₃×A₄×Q₁₆ #11919790

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

Aliases

direct product	C₂×C₃×A₄×Q₁₆
unambiguous semidirect product	(C₂³×Q₁₆)⋊C₃²
unambiguous semidirect product	(C₂³×C₃×Q₁₆)⋊C₃

Fitting	C₂³×C₃×Q₁₆ ⋊ C₃
Sylow	C₂³×Q₁₆ ⋊ C₃²

808 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 176 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, 153801);