Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#10620516 |
| Hall | C32×C7 ⋊ #104 |
| Sylow | C32 ⋊ #6399 |
| Sylow | C7 ⋊ C3×#805 |
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #72246658, C3×D7×#805, #72246681, … |
| maximal normal subgroup of | #72246658, C3×D7×#805, #72246681, … |
Past the SmallGroups library coverage — no SmallGroups id.