Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×#11724243 |
| Fitting | C22×C34 ⋊ C8 |
| Sylow | C34 ⋊ C22⋊C8 |
460 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13180427 |
| maximal normal subgroup of | C3×#13180427 |
Past the SmallGroups library coverage — no SmallGroups id.