Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D29⋊#444 |
| Fitting | C29×#135 ⋊ C4 |
| Sylow | C29 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^17,e^b=eg,h^c=h^12,h^d=h^28,h^f=h^28142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 21281);