Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)×#1142⋊C3 |
| Hall | C7×#1142 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ SD16 |
| Sylow | C72 ⋊ C32×SD16 |
256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #72245397, ΓL(1,𝔽8)×#6495⋊C3, #72245450 |
| maximal normal subgroup of | #72245397, ΓL(1,𝔽8)×#6495⋊C3, #72245450 |
Past the SmallGroups library coverage — no SmallGroups id.