Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#67002 |
| Fitting | C5×C11×#41 ⋊ C2 |
| Hall | C5×C11 ⋊ AGL(1,ℤ/8) |
| Sylow | C11 ⋊ C5×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(17,18)(19,24)(20,22)(21,23);(18,22)(21,24);(7,8)(9,10)(11,12)(13,14)(15,16)(18,21)(19,23)(22,24)305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 885);