Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624727⋊C2 |
| Fitting, Sylow | #10624727 ⋊ C2 |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=f,c^3=e,d^3=f,f^3=g,b^a=bdf^2g^2,c^a=cf^2g^2,d^a=d^2f^2g^2,e^a=eg^2,f^a=f^2g^2,g^a=g^2,c^b=ce,d^c=dg93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1100);