Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C29×#137 ⋊ C4 |
| Sylow | C29 ⋊ #1882 |
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=f,b^2=df,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^17,d^b=dg,f^b=fg,h^b=h^12,e^c=eg,h^f=h^28109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20509);