Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C11 ⋊ AGL(1,ℤ/8) |
| Sylow | C11 ⋊ #4057 |
| Sylow | C5 ⋊ #66967 |
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 440 |
Polycyclic presentation:
2^5,5,11|b^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^10,c^b=cde,d^b=de,f^b=f^4,d^c=de110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 724);