Finite Group Databasebeta

C4×#65838 #12257544

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#65838

Splittings

FittingC2×C4×C5×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4×#520

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC23×C5C25
prime radicalC22×#709C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4×#520
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

3698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 327812);