Finite Group Databasebeta

C4×#65502 #12020448

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC4×#65502

Splittings

FittingC23×C42×C5 ⋊ C2
SylowC5 ⋊ C4×#386

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C22×C42
FrattiniC24C23×D5
FittingC23×C42×C5C2
socle, cosocleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC23×C42D5
hypocenterC5C4×#386
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C23×C42

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 90716);