Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#23782982 |
| derived, Hall | C13×C67 ⋊ C32×C4 |
| Hall | C3×#14579731 ⋊ C4 |
| Hall | Dic871 ⋊ C32 |
| Sylow | C67 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C3×(C67⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10452 |
906 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 84);