Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | ΓL(1,𝔽8)×#908 |
| Fitting | C3×C7×M16 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8) |
| Sylow | C7 ⋊ C3×#908 |
292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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 | AGL(1,𝔽7)×#908, D3×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245617, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#908, D3×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245617, … |
| maximal quotient of | ΓL(1,𝔽8)×#63825 |
Past the SmallGroups library coverage — no SmallGroups id.