Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#10621134 |
| Hall | C32×C7 ⋊ #120 |
| Sylow | C32 ⋊ #6445 |
| Sylow | C7 ⋊ C3×#937 |
574 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | #72247028, C3×D7×#937, #72247074 |
| maximal normal subgroup of | #72247028, C3×D7×#937, #72247074 |
| maximal quotient of | C3×#13054537 |
Past the SmallGroups library coverage — no SmallGroups id.