Finite Group Databasebeta

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C22×D4×C3⋊AGL(1,ℤ/9) #72268922

order5184
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C210×C3

Aliases

direct productC22×D4×C3⋊AGL(1,ℤ/9)

Splittings

FittingC22×C3×D4×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C23×D4

Subgroups

subgroupG/H
centerC23C22×C3⋊AGL(1,ℤ/9)
commutator, cosocleC2×C3×C9C25×C3
FrattiniC2×C3C24×C3×C3⋊D3
FittingC22×C3×D4×3−1+2C2
socleC23×C32C22×C3×D3
hypercenterC22×D4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C23×C3×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×D4

14682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.