Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C32×C9 ⋊ Q8 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^4|a^2=c,b^2=c,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 | #13047639, #13047641, #13047645, … |
| maximal normal subgroup of | #13047639, #13047641, #13047645, … |
| maximal quotient of | #13048010, C4⋊(C3⋊(C3⋊Dic9)), C2×#10619985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 504);