Finite Group Databasebeta

← Prev (#72254992) Next (#72254994) →

D3×#72224648 #72254993

order6144
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productD3×#72224648

Splittings

FittingC3×#72224648 ⋊ C2
SylowC3 ⋊ C2×#72224648

Subgroups

subgroupG/H
centerC2D3×#93877
commutatorC3×C32C22×C16
Frattini#7330C22×D3
FittingC3×#72224648C2
socleC2×C3C2×#93877
prime radicalC22×D3#7457
cosocleC3×#7330C23
hypercenter#72224648D3
hypocenterC3C2×#72224648
LCSG ▷ C3×C32 ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1311 ◁ #7330 ◁ #72224648

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72224662
maximal normal subgroup ofD3×#72224662

GAP

Past the SmallGroups library coverage — no SmallGroups id.