Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C211 |
| direct product | C22×#67006⋊C5 |
| Fitting | C26×C11 ⋊ C2×C5 |
| Hall | C22×#67006 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C22×#120 |
| Sylow | C11 ⋊ C22×C5×#120 |
9088 conjugacy classes of subgroups; only the 1361 normal subgroups are shown.
This group has 9088 conjugacy classes of subgroups — too many to draw. Only its 1361 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
344 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.