Finite Group Databasebeta

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#102×C3⋊AGL(1,ℤ/9) #72254764

order5184
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct product#102×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×3−1+2×#102 ⋊ C2
SylowC3×3−1+2 ⋊ C2×#102

Subgroups

subgroupG/H
centerC22D4×C3⋊AGL(1,ℤ/9)
commutatorC3×C4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×C3⋊D3
FittingC3×3−1+2×#102C2
socleC22×C32C3×D3×D4
prime radicalC2×D4×C3⋊AGL(1,ℤ/9)C2
cosocleC2×C3×C4×C9C23×C3
hypercenter#102C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×#102
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

2245 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

294 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)

GAP

Past the SmallGroups library coverage — no SmallGroups id.