Finite Group Databasebeta

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C22×#65253 #12962953

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#65253

Splittings

SylowC5 ⋊ C22×#428

Subgroups

subgroupG/H
centerC24C2×C22⋊D5
commutatorC4×C5C24×C4
FrattiniC2×C4C24×D5
FittingC23×C5×C4⋊C4C2
socleC24×C5C2×D4
prime radicalC25×C5D4
cosocleC2×C4×C5C25
hypercenterC23×C4⋊C4D5
hypocenterC5C22×#428
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033221);