Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | D3×#62892 |
| Fitting | C3×#62892 ⋊ C2 |
| Sylow | C3 ⋊ C2×#62892 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C26×D3 |
| commutator, socle, cosocle | C22×C3 | C27 |
| Fitting | C3×#62892 | C2 |
| hypercenter | #62892 | D3 |
| hypocenter | C3 | C2×#62892 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #62892 | |
Only the 32171 normal subgroups are shown; non-normal subgroups are omitted.
219 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6533135 |
| maximal normal subgroup of | D3×#6533135 |
| maximal quotient of | D3×#7849701, D3×#7792761, D3×#7918389, … |
Past the SmallGroups library coverage — no SmallGroups id.