Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×D7×D12 |
| Fitting | C3×C4×C72 ⋊ C22 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×D12 |
| Sylow | C3 ⋊ C7×D4×D7 |
264 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D72×D12, D3×C7×D4×D7, D7×#66681, … |
| maximal normal subgroup of | D72×D12, D3×C7×D4×D7, D7×#66681, … |
Past the SmallGroups library coverage — no SmallGroups id.