Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | D7×#3752 |
| Fitting | C2×C32×C4×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ D7×C22⋊C4 |
| Sylow | C7 ⋊ C2×#3752 |
792 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D7×C22⋊C4×C3⋊D3, D7×#64146, D7×#64091, … |
| maximal normal subgroup of | D7×C22⋊C4×C3⋊D3, D7×#64146, D7×#64091, … |
Past the SmallGroups library coverage — no SmallGroups id.