Finite Group DatabasebetaFinite Group Databasebeta| order | 29040 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×#72213693 |
| Fitting | C22×C3×C112 ⋊ C22×C5 |
| Hall | C3×#14515540 ⋊ C5 |
| Hall | #14515540 ⋊ C3×C5 |
| Hall | C3×#10597243 ⋊ C2×D4 |
| Hall | #10597243 ⋊ C2×C3×D4 |
| Hall | C3×C112 ⋊ C2×C5×D4 |
| Sylow | C112 ⋊ C2×C3×C5×D4 |
752 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213693 |
| maximal normal subgroup of | D3×#72213693 |
Past the SmallGroups library coverage — no SmallGroups id.