Finite Group Databasebeta

C4×#65879 #12257533

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

Aliases

direct productC4×#65879

Splittings

FittingC42×C5×D4 ⋊ C2
SylowC5 ⋊ C4×#518

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC42×C5×D4C2
socle, cosocleC23×C5C25
prime radicalC22×D4×D5C22
hypercenterC42×D4D5
hypocenterC5C4×#518
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C42×D4

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 327801);