Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊(D11⋊C25) |
| unambiguous semidirect product | (C11⋊C25)⋊D49 |
| unambiguous semidirect product | D539⋊C25 |
| derived, Hall | C11×C49 ⋊ C2×C25 |
| Hall | C49×C11⋊C25 ⋊ C2 |
| Hall | D539 ⋊ C25 |
| Hall | C11⋊C25 ⋊ D49 |
| Sylow | C49 ⋊ D11⋊C25 |
| Sylow | C11 ⋊ C25×D49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
Polycyclic presentation:
2,5,7,11,5,7|b^5=e,c^7=f^6,c^a=c^6f,d^a=d^10,f^a=f^6,d^b=d^4895 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 4);