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C8×2−1+4⋊C5 #13046046

order1280
automorphism?
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×2−1+4⋊C5
unambiguous semidirect product(C8×2−1+4)⋊C5

Splittings

Fitting, SylowC8×2−1+4 ⋊ C5
derived2−1+4 ⋊ C5×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8C24⋊C5
commutator, hypocenter2−1+4C5×C8
FrattiniC2×C4C2×C24⋊C5
FittingC8×2−1+4C5
socleC22C4×C24⋊C5
prime radicalC2×2−1+4⋊C5C4
cosocleC4×2−1+4C2×C5
LCSG ▷ 2−1+4
UCSC1 ◁ C2×C8

246 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 256

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116314);