Finite Group Databasebeta

← Prev (#13025666) Next (#13025668) →

C4×#64887 #13025667

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#64887

Splittings

SylowC5 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C42C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C16
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC23×C5C22×C8
prime radicalC23×D5C2×C8
cosocleC22×#168C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C4×C22⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095935);