Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic127⋊C7) |
| unambiguous semidirect product | (C127⋊C7)⋊Dic9 |
| unambiguous semidirect product | Dic1143⋊C7 |
| derived, Hall | C9×C127 ⋊ C4×C7 |
| Hall | C9×C127⋊C7 ⋊ C4 |
| Hall | Dic1143 ⋊ C7 |
| Hall | C127⋊C7 ⋊ Dic9 |
| Sylow | C127 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ Dic127⋊C7 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4572 |
Polycyclic presentation:
2,3,7,127,2,3|a^2=e,b^3=f^2,b^a=b^2f,d^a=d^126,f^a=f^2,d^c=d^4246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 17);