Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C8×#92314 |
| Fitting | C2×C8×#6900 ⋊ C2 |
| derived | C92 ⋊ C22×C3×C8 |
| Sylow | #6900 ⋊ C22×C8 |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #97×#92314, #106×#92314, C2×D8×#92314 |
| maximal normal subgroup of | #97×#92314, #106×#92314, C2×D8×#92314 |
Past the SmallGroups library coverage — no SmallGroups id.