Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C9)⋊Dic25 |
| unambiguous semidirect product | Dic775⋊C9 |
| derived, Hall | C25×C31 ⋊ C4×C9 |
| Hall | C25×C31⋊C9 ⋊ C4 |
| Hall | Dic775 ⋊ C9 |
| Hall | C31⋊C9 ⋊ Dic25 |
| Sylow | C31 ⋊ C9×Dic25 |
| Sylow | C25 ⋊ Dic31⋊C9 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,31,2,3,5|a^2=e,b^3=f,c^5=g^4,c^a=c^4g,d^a=d^30,g^a=g^4,d^b=d^251002 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 9);