Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(#13089712⋊C5) |
| unambiguous semidirect product | (C3⋊#13089712)⋊C5 |
| derived, Hall | C3×C112⋊C3 ⋊ C4×C5 |
| Hall | C3×(C112⋊C3)⋊C5 ⋊ C4 |
| Hall | C3⋊#13089712 ⋊ C5 |
| Hall | #10597243 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C5×C3⋊Dic3 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,11^2,2|a^2=g,c^a=c^2,d^a=d^2,f^a=e^4f^10,e^b=e^4,f^b=f^4,e^c=e^7f^10,f^c=e^2f^390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 315);