Finite Group Databasebeta

← Prev (#72244028) Next (#72244030) →

D9×D9⋊H(3,𝔽3) #72244029

order8748
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32

Aliases

direct productD9×D9⋊H(3,𝔽3)

Splittings

Fitting, SylowC9×C9⋊H(3,𝔽3) ⋊ C22

Subgroups

subgroupG/H
centerC3C3×D9×AGL(1,ℤ/9)
commutator, cosocleC3×C92C22×C32
Frattini, socleC33C32×D32
FittingC9×C9⋊H(3,𝔽3)C22
hypercenterC32D9×AGL(1,ℤ/9)
hypocenterC92C22×H(3,𝔽3)
LCSG ▷ C3×C92 ▷ C92
UCSC1 ◁ C3 ◁ C32

1175 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72244059, D9×D9⋊((C3⋊D3)⋊C3)
maximal normal subgroup of#72244059, D9×D9⋊((C3⋊D3)⋊C3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.