Finite Group Databasebeta

← Prev (#13033162) Next (#13033164) →

C22×#64874 #13033163

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#64874

Splittings

FittingC22×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C22×#340

Subgroups

subgroupG/H
centerC24C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC24×C5C22⋊C4
prime radicalC24×D5D4
cosocleC2×C4×D5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C22×#340
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1103431);