Finite Group Databasebeta

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D3×#611⋊C9 #72259798

order3888
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C23

Aliases

direct productD3×#611⋊C9

Splittings

FittingC22×C3×C9⋊C9 ⋊ C22
SylowC3×C9⋊C9 ⋊ C2×D4

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,ℤ/9)
commutatorC2×C3×C9C23×C9
FrattiniC2×C32C2×C3×D32
FittingC22×C3×C9⋊C9C22
socleC2×C33C22×C3×D3
prime radicalC3×D3×#611C3
cosocleC2×C32×C9C23×C3
hypercenterC22×C3D3×AGL(1,ℤ/9)
hypocenterC3×C9C2×D4×C9
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C3 ◁ C22×C3

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#14517439
maximal normal subgroup ofD3×#14517439

GAP

Past the SmallGroups library coverage — no SmallGroups id.