Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×AGL(1,ℤ/9) |
| Fitting, Sylow | C27×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C2×C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C2×C3×C27 |
| Frattini | C3×C9 | C32×D3 |
| Fitting | C27×3−1+2 | C2 |
| socle | C32 | C3×D3×C9 |
| prime radical | C3×AGL(1,ℤ/9) | C9 |
| cosocle | C92 | C2×C32 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C27 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1097);