Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽7)×D24 |
| Fitting | C3×C7×C8 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×C3×D24 |
326 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 77 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, AGL(1,𝔽7)×#914, D3×D8×AGL(1,𝔽7), … |
| maximal normal subgroup of | AGL(1,𝔽7)×#908, AGL(1,𝔽7)×#914, D3×D8×AGL(1,𝔽7) |
| maximal quotient of | AGL(1,𝔽7)×#3714 |
Past the SmallGroups library coverage — no SmallGroups id.