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C4×#64688 #11989803

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#64688

Splittings

FittingC4×C5×C22⋊C8 ⋊ C2
SylowC5 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4#685
commutatorC22×C5C2×C4×C8
FrattiniC23×C4C22×D5
FittingC4×C5×C22⋊C8C2
socleC23×C5C2×C22⋊C4
prime radicalC24×D5C2×C4
cosocleC23×C4×C5C23
hypercenterC4×C22⋊C8D5
hypocenterC5C4×#323
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 60071);