Finite Group DatabasebetaFinite Group Databasebeta| order | 14688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,ℤ/9)×AGL(1,𝔽17) |
| Fitting, Hall | C17×3−1+2 ⋊ C2×C16 |
| derived | C9×C17 ⋊ C2×C3×C16 |
| Sylow | 3−1+2 ⋊ C2×AGL(1,𝔽17) |
| Sylow | C17 ⋊ C16×AGL(1,ℤ/9) |
178 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 153 |
170 conjugacy classes — view the full character table.
| holomorph of | C9×C17 |
Past the SmallGroups library coverage — no SmallGroups id.