Finite Group Databasebeta

C4×#65126 #12097199

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

Aliases

direct productC4×#65126

Splittings

FittingC4×C5×C4⋊C8 ⋊ C2
SylowC5 ⋊ C4×#423

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC22×C5C22×C42
FrattiniC22×C4C23×D5
FittingC4×C5×C4⋊C8C2
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenterC4×C4⋊C8D5
hypocenterC5C4×#423
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1382 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, 167467);