Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C3⋊AGL(1,𝔽13) |
| Fitting, socle | C2×C32×C13 ⋊ C2×C3×C4 |
| derived | C32×C13 ⋊ C22×C3×C4 |
| Hall | C32×C13⋊C3 ⋊ C22×C4 |
| Sylow | C13 ⋊ C2×C3×D3×Dic3 |
580 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C2×D32×AGL(1,𝔽13), #72242015, #72242017 |
| maximal normal subgroup of | C2×D32×AGL(1,𝔽13), #72242015, #72242017 |
| maximal quotient of | #72242015 |
Past the SmallGroups library coverage — no SmallGroups id.