Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#66563⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ SD16 |
| Sylow | C7 ⋊ C32×#214 |
368 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | #72254188, C3×AGL(1,𝔽7)×#214, #72254200, … |
| maximal normal subgroup of | #72254188, C3×AGL(1,𝔽7)×#214, #72254200, … |
Past the SmallGroups library coverage — no SmallGroups id.