Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#4038 |
| Fitting | C5×C11×C4⋊C4 ⋊ C2 |
| Hall | C5×C11 ⋊ #117 |
| Sylow | C5 ⋊ C11×#117 |
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(17,18,19,20)(22,26)(23,27);(21,23,24,27)(22,25,26,28);(13,14)(15,16)(21,22)(23,25)(24,26)(27,28)440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 915);