Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6401 |
| Hall | C5×C7 ⋊ SD32 |
| Sylow | C7 ⋊ C5×SD32 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26);(7,8)(9,10)(11,12)(13,14,17,21)(15,18,24,27)(16,25,23,20)(19,28,26,22)160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 104);