Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | Q8 ⋊ #733 |
49 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^4,2^3|a^3=d^2,b^3=d^2,e^2=g,f^2=g,b^a=bc,c^a=cd,e^a=f,f^a=efg,f^e=fg61 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 95);