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×#731 ⋊ C2 |
| Sylow | #731 ⋊ D4 |
90 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=fg43 conjugacy classes — view the full character table.
| maximal subgroup of | #13047203, #13047204, #13047211, … |
| maximal normal subgroup of | #13047203, #13047204, #13047211, … |
| maximal quotient of | #13046647, #13046650, #13046683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 165);