Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C29×#576 ⋊ C2 |
| Sylow | C29 ⋊ #3288 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,h^b=h^28,f^c=fg,e^d=eg334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 16274);