Finite Group Databasebeta

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C4×#64932 #13025690

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#64932

Splittings

SylowC5 ⋊ C4×#350

Subgroups

subgroupG/H
centerC42C22⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C2×C22⋊C8
prime radicalC2×C5×#41C2×C4
cosocleC22×#168C23
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C4×#350
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095958);