Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×(C22⋊D11)⋊C4 |
| Fitting | C5×C11×C22⋊C4 ⋊ C2 |
| Hall | C5×C11 ⋊ C4×D4 |
| Sylow | C11 ⋊ C4×C5×D4 |
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 880 |
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)(17,18,19,20)(22,24);(21,22)(23,24);(7,8)(9,10)(11,12)(13,14)(15,16)(22,24)350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 818);