Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C22 |
| direct product | C3×C7×#6495 |
| Fitting | C2×C3×C72×D4 ⋊ C2 |
| Hall | C3×C72 ⋊ AGL(1,ℤ/8) |
| Sylow | C72 ⋊ C3×AGL(1,ℤ/8) |
434 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
861 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#72214529, D3×C7×#6495, #72269418 |
| maximal normal subgroup of | C3×#72214529, D3×C7×#6495, #72269418 |
Past the SmallGroups library coverage — no SmallGroups id.