Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | ΓL(1,𝔽8)×#63930 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×SD16 |
| Sylow | C7 ⋊ C3×#63930 |
764 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#63930, ΓL(1,𝔽8)×#10595100, #72269327 |
| maximal normal subgroup of | AGL(1,𝔽7)×#63930, ΓL(1,𝔽8)×#10595100, #72269327 |
Past the SmallGroups library coverage — no SmallGroups id.