Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#63923 |
| Fitting | C2×C32×C4×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ #120 |
| Sylow | C32 ⋊ C7×#120 |
574 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#10595278, D7×#63923, #72247062 |
| maximal normal subgroup of | C7×#10595278, D7×#63923, #72247062 |
| maximal quotient of | C7×#10590397 |
Past the SmallGroups library coverage — no SmallGroups id.