Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72222048 |
| derived | C3×C72 ⋊ C22×C3×C4 |
| Hall | C3×#3861 ⋊ C22×C4 |
| Sylow | C72 ⋊ C2×C3×C4×D3 |
671 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11924174, C2×#72222098, C2×#72222111 |
| maximal normal subgroup of | C2×D3×#11924174, C2×#72222098, C2×#72222111 |
Past the SmallGroups library coverage — no SmallGroups id.