C₂×C₂²⋊((C₂⁴⋊C₅)⋊C₂) #13046178

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	C₂×C₂²⋊((C₂⁴⋊C₅)⋊C₂)
unambiguous semidirect product	C₂³⋊((C₂⁴⋊C₅)⋊C₂)

C₂⁷ ⋊ D₅

4827 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 4827 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

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

μ_t(G) = 40

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116446);