Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×#3717 |
| Hall | C32×ΓL(1,𝔽8) ⋊ SD16 |
| Sylow | C7 ⋊ C3×#3717 |
244 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#63930, AGL(1,𝔽7)×#3717, #72254200, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#63930, AGL(1,𝔽7)×#3717, #72254200, … |
Past the SmallGroups library coverage — no SmallGroups id.