Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11745144 |
| Sylow | C29 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^12,h^d=h^28304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19623);