Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C29 ⋊ #1749 |
412 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,h^a=h^28,c^b=cg,h^b=h^12,h^f=h^28280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 20237);