Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#89519⋊C3 |
| Fitting | C3×C7×#100 ⋊ C2×C3 |
| Hall | #89519 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #453 |
| Sylow | C7 ⋊ C32×#453 |
1008 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽7)×#453, #72246407, D3×#89519⋊C3, … |
| maximal normal subgroup of | C3×AGL(1,𝔽7)×#453, D3×#89519⋊C3, #72254465 |
| maximal quotient of | #72246407 |
Past the SmallGroups library coverage — no SmallGroups id.