Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C17×Dic31 |
| derived, Sylow | C31 ⋊ C3×C4×C5×C17 |
| Hall | C3×C5×C17×C31 ⋊ C4 |
| Hall | C5×C17×C31 ⋊ C3×C4 |
| Hall | C3×C17×C31 ⋊ C4×C5 |
| Hall | C17×C31 ⋊ C3×C4×C5 |
| Hall | C3×C5×C31 ⋊ C4×C17 |
| Hall | C5×C31 ⋊ C3×C4×C17 |
| Hall | C3×C31 ⋊ C4×C5×C17 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31620 |
8670 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 5);