Finite Group DatabasebetaFinite Group Databasebeta| order | 17496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×#72221862 |
| Fitting | C2×#14550484 ⋊ C22 |
| derived | C32⋊C27 ⋊ C23×C9 |
| Sylow | #14550484 ⋊ C23 |
1274 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1274 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
246 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221873 |
Past the SmallGroups library coverage — no SmallGroups id.