C₂³×Q₈×AGL(1,𝔽₅) #13046010

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product	C₂³×Q₈×AGL(1,𝔽₅)
unambiguous semidirect product	D₅⋊(C₂²×C₄×Q₈)

Fitting	C₂³×C₅×Q₈ ⋊ C₄
Sylow	C₅ ⋊ C₂³×C₄×Q₈

12446 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.

normal subgroups only

This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 6264 normal subgroups are shown.

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

μ_t(G) = 320

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116278);