Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊AGL(1,ℤ/9)) |
| Fitting | C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ D4 |
187 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^3|b^2=d,e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^2,g^a=g^2,e^c=eg^275 conjugacy classes — view the full character table.
| maximal subgroup of | #88416⋊C3, #88417⋊C3, #88422⋊C3, … |
| maximal normal subgroup of | #88416⋊C3, #88417⋊C3, #88422⋊C3, … |
| maximal quotient of | #13047905, #13047908, #13047909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 483);