Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊(Dic13⋊C3) |
| unambiguous semidirect product | Dic1573⋊C3 |
| derived, Hall | C13×C121 ⋊ C3×C4 |
| Hall | Dic1573 ⋊ C3 |
| Hall | C13⋊C3×C121 ⋊ C4 |
| Sylow | C121 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ Dic121 |
| Sylow | C13 ⋊ C3×Dic121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6292 |
Polycyclic presentation:
2,3,11,13,2,11|a^2=e,c^11=f^10,c^a=c^10f,d^a=d^12,f^a=f^10,d^b=d^3856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 4);