Finite Group DatabasebetaFinite Group Databasebeta| order | 2800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22×C5 |
| direct product | C7×C22⋊#1044 |
| Fitting | C22×C52×C7 ⋊ C4 |
| Hall | C52×C7 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C7×C22⋊C4 |
200 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11717375, D7×C22⋊#1044, #72243111, … |
| maximal normal subgroup of | C7×#11717375, D7×C22⋊#1044, #72243111, … |
Past the SmallGroups library coverage — no SmallGroups id.