Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C9)⋊#1035 |
| unambiguous semidirect product | (C31⋊#1035)⋊C9 |
| derived, Hall | C25×C31 ⋊ C4×C9 |
| Hall | C25×C31⋊C9 ⋊ C4 |
| Hall | C31⋊#1035 ⋊ C9 |
| Hall | C31⋊C9 ⋊ #1035 |
| Sylow | C31 ⋊ C9×#1035 |
| Sylow | C25 ⋊ Dic31⋊C9 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,31,3,5|a^2=c,b^3=f,d^5=g,d^a=d^2g,e^a=e^30,g^a=g^2,e^b=e^5,d^c=d^4g^4,g^c=g^4300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 26);