Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C29×#423 ⋊ C2 |
| Sylow | C29 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^7,29|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^b=h^28,d^c=dg,h^c=h^28442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 13245);