Finite Group Databasebeta

D4×#3963 #12020770

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productD4×#3963

Splittings

SylowC5 ⋊ D4×#95

Subgroups

subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC22×C4×C5×D4C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC22×C4×D4D5
hypocenterC5D4×#95
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×D4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 91038);