Finite Group DatabasebetaFinite Group Databasebeta| order | 8748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×#72221799 |
| Fitting | C2×#14546335 ⋊ C2 |
| derived | C81 ⋊ C22×C27 |
| Sylow | #14546335 ⋊ C22 |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
188 conjugacy classes — view the full character table.
| holomorph of | C2×C81 |
Past the SmallGroups library coverage — no SmallGroups id.