Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#6399⋊C3 |
| Fitting | C3×C7×M16 ⋊ C2×C3 |
| Hall | #6399 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #104 |
| Sylow | C7 ⋊ C32×#104 |
264 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 86 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×#89519⋊C3, C3×#89970⋊C3, C3×#104×AGL(1,𝔽7), … |
| maximal normal subgroup of | C3×#89519⋊C3, C3×#89970⋊C3, C3×#104×AGL(1,𝔽7), … |
| maximal quotient of | #72246386 |
Past the SmallGroups library coverage — no SmallGroups id.