Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#66557⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ M16 |
| Sylow | C7 ⋊ C32×#208 |
368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #72254145, C3×AGL(1,𝔽7)×#208, #72254166, … |
| maximal normal subgroup of | #72254145, C3×AGL(1,𝔽7)×#208, #72254166, … |
Past the SmallGroups library coverage — no SmallGroups id.