Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#6510 |
| Fitting | C2×C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ #124 |
| Sylow | C7 ⋊ C5×#124 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(14,16)(17,19,20,24)(18,22,21,23);(17,18,20,21)(19,23,24,22);(7,8)(9,10)(11,12)(13,14)(15,16)(18,21)(22,23)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 711);