Finite Group Databasebeta

C8×#4053 #12064889

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#4053

Splittings

FittingC5×C8×M16 ⋊ C2
SylowC5 ⋊ C8×#131

Subgroups

subgroupG/H
centerC4×C8C22×D5
commutatorC2×C5C22×C4×C8
FrattiniC42C23×D5
FittingC5×C8×M16C2
socleC22×C5C22×C42
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenterC8×M16D5
hypocenterC5C8×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C8 ◁ C8×M16

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 135157);