Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6408 |
| Hall | C5×C7 ⋊ #99 |
| Sylow | C7 ⋊ C5×#99 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(13,15)(14,17)(16,20)(18,19);(7,8)(9,10)(11,12)(13,14)(15,19,20,17)(16,18)205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 109);