Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | Q8×H(3,𝔽3) ⋊ C3 |
| Sylow | Q8 ⋊ AΣL(1,𝔽27) |
71 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
3^4,2^3|e^2=g,f^2=g,b^a=bc,e^a=f,f^a=efg,c^b=cd,f^e=fg45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 99);