Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D4 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^4|d^3=g,b^a=bc,d^a=d^2g^2,e^a=e^2,f^a=f^2,g^a=g^2165 conjugacy classes — view the full character table.
| maximal subgroup of | #13048688, #13048691, #13048697, … |
| maximal normal subgroup of | #13048688, #13048691, #13048697, … |
| maximal quotient of | #13048010, #13048012, #13048019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 511);