Finite Group Databasebeta

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C4×#65791 #13043115

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#65791

Splittings

SylowC5 ⋊ C4×#504

Subgroups

subgroupG/H
centerC42C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C23×C8
prime radicalC2×C5×#41C2×C4
cosocleC2×#168C24
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C4×#504
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C4×#41

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113383);