Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C49⋊C3)⋊#1039 |
| derived, Hall | C52×C49 ⋊ C3×C4 |
| Hall | C49⋊#1039 ⋊ C3 |
| Hall | C52×C49⋊C3 ⋊ C4 |
| Hall | C49⋊C3 ⋊ #1039 |
| Sylow | C49 ⋊ C3×#1039 |
| Sylow | C52 ⋊ (C49⋊C3)⋊C4 |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7,2,7|a^2=f,e^7=g^6,c^a=c^4,d^a=d^4,e^a=e^6g,g^a=g^6,e^b=e^4g^5,g^b=g^4484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 48);