Finite Group Databasebeta

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D9×#3292 #72268989

order2304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD9×#3292

Splittings

FittingC9×#3292 ⋊ C2
SylowC9 ⋊ C2×#3292

Subgroups

subgroupG/H
centerC2D42×D9
commutator, cosocleC2×C4×C9C25
FrattiniC2×C3×C4C24×D3
FittingC9×#3292C2
socleC2×C3D3×D42
hypercenter#3292D9
hypocenterC9C2×#3292
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #3292

4149 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×#61110
maximal normal subgroup ofD9×#61110

GAP

Past the SmallGroups library coverage — no SmallGroups id.