Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26 |
| direct product | #135×C22⋊A4 |
| Fitting, Sylow | C24×#135 ⋊ C3 |
20069 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 20069 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A42×#135 |
| maximal normal subgroup of | A42×#135 |
Past the SmallGroups library coverage — no SmallGroups id.