Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#11924207 |
| Fitting | C23×C3×C72 ⋊ C2×C3 |
| Hall | C2×C7×C22⋊D7 ⋊ C32 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C32×D4 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
318 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#72210376, C2×D3×#11924207, C2×#72222098 |
| maximal normal subgroup of | C2×C3×#72210376, C2×D3×#11924207, C2×#72222098 |
Past the SmallGroups library coverage — no SmallGroups id.