Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×AGL(1,ℤ/27) |
| Fitting, Hall | C5×#6875 ⋊ C2 |
| derived | C27 ⋊ C2×C5×C9 |
| Sylow | #6875 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,ℤ/27) |
| commutator, hypocenter | C27 | C2×C5×C9 |
| Frattini | C3×C9 | C3×C5×D3 |
| Fitting | C5×#6875 | C2 |
| socle | C3×C5 | D9⋊C9 |
| prime radical | C5×D27⋊C3 | C3 |
| cosocle | C27⋊C3 | C2×C3×C5 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,ℤ/27) |
| maximal normal subgroup of | D5×AGL(1,ℤ/27) |
Past the SmallGroups library coverage — no SmallGroups id.