Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | ΓL(1,𝔽8)×#806 |
| Fitting | C3×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #99 |
| Sylow | C7 ⋊ C3×#806 |
242 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×ΓL(1,𝔽8)×#99, AGL(1,𝔽7)×#806, #72254408, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×#99, AGL(1,𝔽7)×#806, #72254408, … |
Past the SmallGroups library coverage — no SmallGroups id.