Finite Group Databasebeta

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C22×#65382 #12968491

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22×#65382

Splittings

SylowC5 ⋊ C22×#487

Subgroups

subgroupG/H
centerC24C2×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×C4⋊Q8C2
socle, prime radicalC24×C5C2×D4
hypercenterC22×C4⋊Q8D5
hypocenterC5C22×#487
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

2398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 1038759);