Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C121⋊C5)⋊Dic13 |
| unambiguous semidirect product | Dic1573⋊C5 |
| derived, Hall | C13×C121 ⋊ C4×C5 |
| Hall | C13×C121⋊C5 ⋊ C4 |
| Hall | Dic1573 ⋊ C5 |
| Hall | C121⋊C5 ⋊ Dic13 |
| Sylow | C121 ⋊ C5×Dic13 |
| Sylow | C13 ⋊ Dic121⋊C5 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6292 |
Polycyclic presentation:
2,5,11,13,2,11|a^2=e,c^11=f^10,c^a=c^10f,d^a=d^12,f^a=f^10,c^b=c^4f^4,f^b=f^4392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 4);