Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C3×C79⋊C3)⋊C27 |
| Fitting | C3×C27×C79 ⋊ C3 |
| Sylow | C79 ⋊ C32⋊C27 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6399 |
Polycyclic presentation:
3^5,79|a^3=d,d^3=e,b^a=bc,f^b=f^232205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 93);