Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×#72229244 |
| Sylow | C25 ⋊ #6875 |
750 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72229286 |
| maximal normal subgroup of | C2×#72229286 |
Past the SmallGroups library coverage — no SmallGroups id.