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×#732 ⋊ C2 |
| Sylow | #732 ⋊ D4 |
95 conjugacy classes of subgroups.
| 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=ef,f^c=fg^243 conjugacy classes — view the full character table.
| maximal subgroup of | #13047216, #13047217, #13047224, … |
| maximal normal subgroup of | #13047216, #13047217, #13047224, … |
| maximal quotient of | #13046659, #13046662, #13046687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 169);