Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic31⋊C25) |
| unambiguous semidirect product | (C31⋊C25)⋊Dic9 |
| unambiguous semidirect product | Dic279⋊C25 |
| derived, Hall | C9×C31 ⋊ C4×C25 |
| Hall | C9×C31⋊C25 ⋊ C4 |
| Hall | Dic279 ⋊ C25 |
| Hall | C31⋊C25 ⋊ Dic9 |
| Sylow | C31 ⋊ C25×Dic9 |
| Sylow | C9 ⋊ Dic31⋊C25 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,31,2,3,5|a^2=e,b^5=g,c^3=f^2,c^a=c^2f,d^a=d^30,f^a=f^2,d^b=d^16570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 6);