Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6450 |
| Hall | C5×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ C4×C5×Q8 |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1120 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(13,15,16,14)(19,23)(21,24);(17,19,20,23)(18,21,22,24);(7,8)(9,10)(11,12)(13,14,16,15)(17,18,20,22)(19,21,23,24)250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 651);