Finite Group Databasebeta

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C4×D4×C3⋊AGL(1,ℤ/9) #72254753

order5184
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC4×D4×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×C4×D4×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊AGL(1,ℤ/9)
commutatorC2×C3×C9C23×C3×C4
FrattiniC22×C3C23×C3×C3⋊D3
FittingC3×C4×D4×3−1+2C2
socleC22×C32C23×C3×D3
prime radicalC2×D4×C3⋊AGL(1,ℤ/9)C2
cosocleC22×C3×C9C24×C3
hypercenterC4×D4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C4×D4

4683 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.

Relationships

maximal subgroup of#442×C3⋊AGL(1,ℤ/9)
maximal normal subgroup of#442×C3⋊AGL(1,ℤ/9)
maximal quotient of#442×C3⋊AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.