Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#4093 |
| Fitting | C2×C5×Q8×C11 ⋊ C2 |
| Hall | C5×C11 ⋊ #124 |
| Sylow | C5 ⋊ C11×#124 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 880 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(18,20)(21,23,24,28)(22,26,25,27);(21,22,24,25)(23,27,28,26);(13,14)(15,16)(17,18)(19,20)(22,25)(26,27)374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 969);