Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C22 |
| direct product | C7×C22⋊#170 |
| unambiguous semidirect product | C22⋊(C7×#170) |
| Hall | C5×C7 ⋊ C22⋊C8 |
| Sylow | C5 ⋊ C7×C22⋊C8 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7)(8,9,10,12,11)(14,16);(9,10,11,12)(13,14)(15,16)(17,18,19,21,20,22,23,24)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 270);