Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220×C4 |
| direct product | C23×D3×#127 |
| Fitting | C23×C3×#127 ⋊ C2 |
| Sylow | C3 ⋊ C24×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C23×D3 |
| commutator, cosocle | C22×C3 | C27 |
| Frattini | C22 | C26×D3 |
| Fitting | C23×C3×#127 | C2 |
| socle | C25×C3 | C24 |
| hypercenter | C23×#127 | D3 |
| hypocenter | C3 | C24×#127 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C25 ◁ C23×#127 | |
259716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#23906 |
| maximal normal subgroup of | C2×D3×#23906 |
Past the SmallGroups library coverage — no SmallGroups id.