Finite Group Databasebeta

← Prev (#13033360) Next (#13033362) →

C2×C4×#4005 #13033361

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#4005

Splittings

SylowC5 ⋊ C2×C4×#101

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C2×C4×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1103629);