Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×C3⋊AGL(1,𝔽13) |
| derived | C32×C13 ⋊ C3×C42 |
| Hall | C32×C13⋊C3 ⋊ C42 |
| Sylow | C13 ⋊ C3×Dic32 |
356 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #624×AGL(1,𝔽13), #72242015, #72242017 |
| maximal normal subgroup of | #624×AGL(1,𝔽13), #72242015, #72242017 |
Past the SmallGroups library coverage — no SmallGroups id.