Finite Group Databasebeta

← Prev (#14415719) Next (#14415721) →

D12×#676 #14415720

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD12×#676

Splittings

FittingC3×C4×C5×C8 ⋊ C22
HallC3×C5 ⋊ D4×M16
SylowC5 ⋊ M16×D12
SylowC3 ⋊ D4×#676

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C4×C5×C8C22
prime radicalC2×D5×D12C4
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×C8

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141418);