Finite Group DatabasebetaFinite Group Databasebeta| order | 10206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C32 |
| direct product | AGL(1,𝔽7)×#6875 |
| Fitting | C7×#6875 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×#6875 ⋊ C2 |
| Hall | D7 ⋊ C3×#6875 |
| Sylow | C7 ⋊ C2×C3×#6875 |
424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×AGL(1,ℤ/27) |
| maximal normal subgroup of | AGL(1,𝔽7)×AGL(1,ℤ/27) |
Past the SmallGroups library coverage — no SmallGroups id.