Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C11 ⋊ #131 |
| Sylow | C11 ⋊ #4131 |
| Sylow | C5 ⋊ #66960 |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 880 |
Polycyclic presentation:
2^5,5,11|b^2=d,d^2=e,c^a=ce,g^a=g^10,c^b=ce,f^b=f^2,f^d=f^495 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1124);