Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊AGL(1,𝔽9) |
| unambiguous semidirect product | C3⋊(C3×AGL(1,𝔽9)) |
| Fitting, socle, Sylow | C34 ⋊ C8 |
| derived | C33 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,𝔽9) |
| commutator, hypocenter | C33 | C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C34 | C8 |
| prime radical | C32×C3⋊D3 | C4 |
| cosocle | C3×#157 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 708);