Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊D289 |
| unambiguous semidirect product | C289⋊(D7⋊C9) |
| unambiguous semidirect product | D2023⋊C9 |
| derived, Hall | C7×C289 ⋊ C2×C9 |
| Hall | C7⋊C9×C289 ⋊ C2 |
| Hall | D2023 ⋊ C9 |
| Sylow | C289 ⋊ D7⋊C9 |
| Hall | C7⋊C9 ⋊ D289 |
| Sylow | C7 ⋊ C9×D289 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18207 |
Polycyclic presentation:
2,3,7,17,3,17|b^3=e,d^17=f^16,c^a=c^6,d^a=d^16f,f^a=f^16,c^b=c^22181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 4);