Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624799⋊C2 |
| Fitting, Sylow | #10624799 ⋊ C2 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=e,d^3=g,c^a=c^2e^2,e^a=e^2,c^b=ce,d^b=df,f^b=fg,f^d=fg62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1311);