Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C3×AΣL(1,𝔽27)×C43⋊C3 |
| Fitting | C3×C43×AΣL(1,𝔽27) ⋊ C3 |
| Sylow | C43 ⋊ C32×AΣL(1,𝔽27) |
2672 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1161 |
867 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 3898);