Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#6500 |
| Fitting | C2×C32×C7×D4 ⋊ C2 |
| Hall | C32×C7 ⋊ #120 |
| Sylow | C7 ⋊ C32×#120 |
780 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#6500, C32×D7×#120, #72246776, … |
| maximal normal subgroup of | C3⋊D3×#6500, C32×D7×#120, #72246776, … |
Past the SmallGroups library coverage — no SmallGroups id.