Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#261×AGL(1,ℤ/9) |
| Fitting | C2×C13×3−1+2 ⋊ C2×C4 |
| derived | C9×C13 ⋊ C22×C3×C4 |
| Hall | C13×3−1+2 ⋊ C22×C4 |
| Sylow | 3−1+2 ⋊ C22×#261 |
| Sylow | C13 ⋊ C2×C4×AGL(1,ℤ/9) |
340 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 234 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,ℤ/9)×AGL(1,𝔽13) |
| maximal normal subgroup of | C2×AGL(1,ℤ/9)×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.