Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C3×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ D4 |
205 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^3|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 | #88658⋊C3, #88662⋊C3, #67×AGL(1,ℤ/9), … |
| maximal normal subgroup of | #88658⋊C3, #88662⋊C3, #67×AGL(1,ℤ/9), … |
| maximal quotient of | #13047947, #13047949, #13047970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 499);