Finite Group Databasebeta

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#97×C3⋊AGL(1,ℤ/9) #72254609

order5184
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C3

Aliases

direct product#97×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×3−1+2×#97 ⋊ C2
SylowC3×3−1+2 ⋊ C2×#97

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊AGL(1,ℤ/9)
commutatorC2×C3×C9C2×C3×C42
FrattiniC2×C3×C4C22×C3×C3⋊D3
FittingC3×3−1+2×#97C2
socleC22×C32C2×C3×C4×D3
prime radicalC22×C3⋊AGL(1,ℤ/9)C2×C4
cosocleC2×C3×C4×C9C23×C3
hypercenter#97C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×#97
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ #97

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 864

Conjugacy classes & character table

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

Relationships

maximal subgroup of#97×#92314, #442×C3⋊AGL(1,ℤ/9)
maximal normal subgroup of#442×C3⋊AGL(1,ℤ/9)
maximal quotient of#97×#92314

GAP

Past the SmallGroups library coverage — no SmallGroups id.