Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#14559051 |
| derived, Hall | C9×C112 ⋊ C4×C5 |
| Hall | C9×#10597243 ⋊ C4 |
| Hall | C9⋊(C11⋊Dic11) ⋊ C5 |
| Hall | #10597243 ⋊ Dic9 |
| Sylow | C112 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ #14559051 |
252 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,11^2,2,3|a^2=f,c^3=g^2,c^a=c^2g,d^a=d^10,e^a=e^10,g^a=g^2,d^b=d^4,e^b=e^4276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 136);