Finite Group Databasebeta

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C2×#10615845 #12965756

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#10615845

Splittings

FittingC22×C5×2−1+4 ⋊ C2
SylowC5 ⋊ C2×#3013

Subgroups

subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×2−1+4C2
socleC23×C5C22×D4
hypercenterC22×2−1+4D5
hypocenterC5C2×#3013
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×2−1+4

4782 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, 1036024);