Finite Group Databasebeta

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C22⋊C4×#674 #13025728

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×#674

Splittings

SylowC5 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C16
FittingC4×C5×C22⋊C4C4
socleC23×C5C22×C8
prime radicalC24×C5C2×C8
cosocleC22×#168C23
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5C16×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1095996);