Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#72219717 |
| Fitting | C23×C34 ⋊ D4 |
| Sylow | C34 ⋊ C2×#120 |
11909 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 11909 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
180 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.