Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C4 |
| direct product | ΓL(1,𝔽8)×#940 |
| Fitting | C2×C3×C7×D4 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #127 |
| Sylow | C7 ⋊ C3×#940 |
486 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#940, D3×ΓL(1,𝔽8)×#127, #72244257, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#940, D3×ΓL(1,𝔽8)×#127, #72244257, … |
| maximal quotient of | ΓL(1,𝔽8)×#64149 |
Past the SmallGroups library coverage — no SmallGroups id.