Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | #123×C11⋊C5 |
| unambiguous semidirect product | (C11×#123)⋊C5 |
| Fitting, Hall | C11×#123 ⋊ C5 |
| Sylow | C11 ⋊ C5×#123 |
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,4)(6,9)(7,11)(14,15,17,20,19)(16,18,22,23,21);(5,6)(7,10)(8,9)(11,12)(13,14,16,19,15,17,21,23,18,20,22);(1,2)(3,4)(5,7,8,11)(6,10,9,12)98 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#525, #123×AGL(1,𝔽11), #72248838, … |
| maximal normal subgroup of | C11⋊C5×#525, #123×AGL(1,𝔽11), #72248838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 404);