Finite Group Databasebeta

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C2×#10602415 #12065699

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#10602415

Splittings

SylowC5 ⋊ C2×#1487

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC22×C4×C5×Q8C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC42×C5C24
hypercenterC22×C4×Q8D5
hypocenterC5C2×#1487
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

1282 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, 135967);