Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C31⋊C9)⋊C81 |
| Sylow | C31 ⋊ C9⋊C81 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22599 |
Polycyclic presentation:
3^6,31|a^3=d,b^3=c,d^3=e,e^3=f,b^a=bc,g^b=g^252727 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 820);