Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | D3×#8546 |
| Fitting | C3×#8546 ⋊ C2 |
| Sylow | C3 ⋊ C2×#8546 |
13748 conjugacy classes of subgroups; only the 473 normal subgroups are shown.
This group has 13748 conjugacy classes of subgroups — too many to draw. Only its 473 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#245233, D3×#347047 |
| maximal normal subgroup of | D3×#245233, D3×#347047 |
| maximal quotient of | D3×#111516 |
Past the SmallGroups library coverage — no SmallGroups id.