Finite Group DatabasebetaFinite Group Databasebeta| order | 20412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | AGL(1,𝔽7)×AGL(1,ℤ/27) |
| Fitting | C7×#6875 ⋊ C22×C3 |
| derived | C7×C27 ⋊ C22×C3×C9 |
| Hall | ΓL(1,𝔽8)×#6875 ⋊ C22 |
| Sylow | C7 ⋊ C2×C3×AGL(1,ℤ/27) |
532 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 189 |
217 conjugacy classes — view the full character table.
| holomorph of | C7×C27 |
Past the SmallGroups library coverage — no SmallGroups id.