Finite Group Databasebeta

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C4×#65136 #12106908

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#65136

Splittings

FittingC4×C5×C4⋊C8 ⋊ C2
SylowC5 ⋊ C4×#478

Subgroups

subgroupG/H
centerC22×C4C2×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×C4⋊C8C2
socleC23×C5C22×D4
prime radicalC22×D20C23
cosocleC22×C4×C5C24
hypercenterC4×C4⋊C8D5
hypocenterC5C4×#478
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 177176);