Finite Group Databasebeta

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C22×#64898 #13043175

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#64898

Splittings

SylowC5 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC23×C5C22⋊C8
prime radicalC22×#709C4
cosocleC2×#168C24
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22×#350
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

1174 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, 1113443);