Finite Group DatabasebetaFinite Group Databasebeta| order | 6720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×D3×C7×AGL(1,𝔽5) |
| Fitting | C2×C3×C4×C5×C7 ⋊ C2×C4 |
| derived, Hall | C3×C5 ⋊ C22×C42×C7 |
| Hall | C3×C5×C7 ⋊ C22×C42 |
| Hall | C5×C7 ⋊ C2×C42×D3 |
| Hall | C3×C7 ⋊ C22×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C42×D3×C7 |
| Sylow | C3 ⋊ C22×C4×C7×AGL(1,𝔽5) |
1992 conjugacy classes of subgroups.
840 conjugacy classes. The character table is too large to display.
| automorphism group of | C29×Dic15 |
Past the SmallGroups library coverage — no SmallGroups id.