Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C29×#127 ⋊ C4 |
| Sylow | C29 ⋊ #1406 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=d,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^12,c^b=cf,d^b=defg,e^b=eg,d^c=dfg,e^d=eg,h^d=h^28112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19637);