Finite Group Databasebeta

← Prev (#14414615) Next (#14414617) →

D4×#6648 #14414616

order1920
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD4×#6648

Splittings

HallC3×C5 ⋊ C2×C8×D4
SylowC5 ⋊ D3×C8×D4
SylowC3 ⋊ C8×D4×D5

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutatorC2×C3×C5C23×C8
FittingC3×C4×C5×D4C22
socleC22×C3×C5C23×C4
prime radicalC2×D4×D15C4
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5C2×C8×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×D4

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 140314);