Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C11×C4⋊C4 ⋊ C2 |
| Hall | C5×C11 ⋊ C22⋊Q8 |
| Sylow | C11 ⋊ #4042 |
| Sylow | C5 ⋊ #66949 |
148 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 880 |
Polycyclic presentation:
2^5,5,11|a^2=e,b^2=e,c^2=e,c^a=ce,f^a=f^4,g^a=g^10,c^b=cd284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 996);