Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×#6445⋊C3 |
| Fitting | C3×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | #6445 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #120 |
| Sylow | C7 ⋊ C32×#120 |
780 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#120×AGL(1,𝔽7), D3×#6445⋊C3, #72244221, … |
| maximal normal subgroup of | C3×#120×AGL(1,𝔽7), D3×#6445⋊C3, #72244221, … |
| maximal quotient of | C3×#89519⋊C3, C3×#89594⋊C3, #72246104, … |
Past the SmallGroups library coverage — no SmallGroups id.