Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#10620874 |
| Hall | C32×C7 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ #6471 |
| Sylow | C7 ⋊ C3×#932 |
326 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #72245859, C3×D7×#932, #72245955, … |
| maximal normal subgroup of | #72245859, C3×D7×#932, #72245955, … |
Past the SmallGroups library coverage — no SmallGroups id.