Finite Group Databasebeta

← Prev (#72244056) Next (#72244058) →

C2×H(3,𝔽3)×AGL(1,ℤ/9) #72244057

order2916
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34

Aliases

direct productC2×H(3,𝔽3)×AGL(1,ℤ/9)

Splittings

FittingC2×H(3,𝔽3)×3−1+2 ⋊ C2
SylowH(3,𝔽3)×3−1+2 ⋊ C22

Subgroups

subgroupG/H
centerC2×C3C32×AGL(1,ℤ/9)
commutator, cosocleC3×C9C22×C33
FrattiniC32C2×C33×D3
FittingC2×H(3,𝔽3)×3−1+2C2
socleC2×C32C33×D3
hypercenterC2×H(3,𝔽3)AGL(1,ℤ/9)
hypocenterC9C22×C3×H(3,𝔽3)
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C2×H(3,𝔽3)

1294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×H(3,𝔽3)×AGL(1,ℤ/9), C2×(C3⋊D3)⋊C3×AGL(1,ℤ/9)
maximal normal subgroup ofC2×(C3⋊D3)⋊C3×AGL(1,ℤ/9)
maximal quotient ofD3×H(3,𝔽3)×AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.