Finite Group Databasebeta

← Prev (#72243243) Next (#72243245) →

3−1+2×D9⋊C9 #72243244

order4374
automorphism?
homologyAbelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×D9⋊C9

Splittings

Fitting, Sylow3−1+2×C9⋊C9 ⋊ C2

Subgroups

subgroupG/H
centerC32C32×AGL(1,ℤ/9)
commutatorC3×C9C2×C32×C9
Frattini, socleC33C33×D3
Fitting3−1+2×C9⋊C9C2
prime radicalC33×D9C32
cosocleC32×C9C2×C33
hypercenterC3×3−1+2AGL(1,ℤ/9)
hypocenterC9C2×C9×3−1+2
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C32 ◁ C3×3−1+2

913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

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

Relationships

maximal subgroup of3−1+2×#92265, AGL(1,ℤ/9)×D9⋊C9
maximal normal subgroup of3−1+2×#92265, AGL(1,ℤ/9)×D9⋊C9

GAP

Past the SmallGroups library coverage — no SmallGroups id.