C₅×A₄×C₄⋊Q₈ #14511331

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₅×A₄×C₄⋊Q₈
unambiguous semidirect product	C₄⋊(C₅×Q₈×A₄)
unambiguous semidirect product	(C₂²×C₄⋊Q₈)⋊(C₃×C₅)
unambiguous semidirect product	(C₂²×C₅×C₄⋊Q₈)⋊C₃

Fitting, Hall	C₂²×C₅×C₄⋊Q₈ ⋊ C₃
Sylow	C₂²×C₄⋊Q₈ ⋊ C₃×C₅

768 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

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

μ_t(G) = 480

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237029);