Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #1579 |
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^17,d^b=df,h^b=h^28,h^c=h^12,h^e=h^28142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20105);