Finite Group Databasebeta

← Prev (#12106160) Next (#12106162) →

C4×#65489 #12106161

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#65489

Splittings

SylowC5 ⋊ C4×#471

Subgroups

subgroupG/H
centerC2×C4#4085
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×AGL(1,ℤ/8)C2
socleC22×C5C2×#121
prime radicalC2×C5×AGL(1,ℤ/8)C22
cosocleC22×C4×C5C24
hypercenterC4×AGL(1,ℤ/8)D5
hypocenterC5C4×#471
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

914 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, 176429);