Finite Group DatabasebetaFinite Group Databasebeta| order | 31424 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C491⋊#338 |
| Sylow | C491 ⋊ #338 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^6,491|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^4904922 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31424, 307);