Finite Group Databasebeta

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C22×#65134 #12966109

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#65134

Splittings

FittingC22×C5×C4⋊C8 ⋊ C2
SylowC5 ⋊ C22×#464

Subgroups

subgroupG/H
centerC24C2×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×C4⋊C8C2
socleC24×C5C2×D4
prime radicalC23×D20C22
hypercenterC22×C4⋊C8D5
hypocenterC5C22×#464
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2918 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, 1036377);