Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | D3×#63045 |
| Fitting | C3×#63045 ⋊ C2 |
| Sylow | C3 ⋊ C2×#63045 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C26×D3 |
| commutator, socle, cosocle | C22×C3 | C27 |
| Fitting | C3×#63045 | C2 |
| hypercenter | #63045 | D3 |
| hypocenter | C3 | C2×#63045 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #63045 | |
Only the 32113 normal subgroups are shown; non-normal subgroups are omitted.
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#511825 |
| maximal normal subgroup of | D3×#511825 |
| maximal quotient of | D3×#7695992, D3×#7659307 |
Past the SmallGroups library coverage — no SmallGroups id.