Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | AΣL(1,𝔽27) ⋊ Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^3|a^2=d,b^2=d,b^a=bd,e^a=e^2,f^a=f^2g,e^c=ef,f^e=fg61 conjugacy classes — view the full character table.
| maximal subgroup of | #13046416, #13046420, #13046422, … |
| maximal normal subgroup of | #13046416, #13046420, #13046422, … |
| maximal quotient of | #13046632, C4⋊#66321, C2×#10619607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 126);