Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | D3×#89039 |
| Fitting | C22×C34 ⋊ C23 |
| Sylow | C34 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×C3⋊D3 |
| commutator, socle, cosocle | C2×C34 | C24 |
| Fitting | C22×C34 | C23 |
| hypercenter | C22 | D32×C3⋊D3 |
| hypocenter | C34 | C22×D4 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 ◁ C22 | |
4946 conjugacy classes of subgroups.
153 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.