Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#6409 |
| Hall | C5×C7 ⋊ #103 |
| Sylow | C7 ⋊ C5×#103 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1120 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(17,18,20,22)(19,24,23,21);(7,8)(9,10)(11,12)(13,14,15,16)(18,21)(19,23)(22,24)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 112);