Finite Group Databasebeta

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C2×#10604021 #13043502

order1280
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×#10604021

Splittings

SylowC5 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C23×C16
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5C22×C8
prime radicalC22×D20C8
cosocleC2×#168C24
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5C2×D4×C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

806 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, 1113770);