Finite Group Databasebeta

C4×#65416 #12097645

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#65416

Splittings

FittingC2×C4×C5×M16 ⋊ C2
SylowC5 ⋊ C4×#435

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC22×C5C22×C42
FrattiniC22×C4C23×D5
FittingC2×C4×C5×M16C2
socleC23×C5C23×C4
prime radicalC22×C22⋊D5C2×C4
cosocleC22×C4×C5C24
hypercenterC2×C4×M16D5
hypocenterC5C4×#435
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 167913);