Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C73×C32⋊C9 ⋊ C3 |
| Sylow | C73 ⋊ H(3,𝔽3)⋊C9 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5913 |
Polycyclic presentation:
3^5,73|a^3=d,b^a=bc,c^a=ce,c^b=ce,f^b=f^8843 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 103);