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D3×C9×AGL(1,ℤ/9) #72243305

order2916
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct productD3×C9×AGL(1,ℤ/9)

Splittings

Fitting, SylowC3×C9×3−1+2 ⋊ C22
derivedC3×C9 ⋊ C22×C3×C9

Subgroups

subgroupG/H
center, hypercenterC9D3×AGL(1,ℤ/9)
commutator, hypocenterC3×C9C22×C3×C9
FrattiniC32C32×D32
FittingC3×C9×3−1+2C22
socleC33C2×C32×D3
prime radicalC3×D3×AGL(1,ℤ/9)C3
cosocleC32×C9C22×C32
LCSG ▷ C3×C9
UCSC1 ◁ C9

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×#92265⋊C2, D3×3−1+2×AGL(1,ℤ/9), C9×D9×AGL(1,ℤ/9), …
maximal normal subgroup ofD3×3−1+2×AGL(1,ℤ/9), D3×D9×AGL(1,ℤ/9)
maximal quotient ofC9×#92265⋊C2, C9×D9×AGL(1,ℤ/9), AGL(1,ℤ/9)×D9⋊C9, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.