Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C7×#3990 |
| Hall | C5×C7 ⋊ M32 |
| Sylow | C5 ⋊ C7×M32 |
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)(8,9,10,12,11)(13,15,17,24,18,16,23,25)(14,19,20,26,21,22,27,28);(9,10,11,12)(13,14,16,19,17,20,25,26,18,21,15,22,23,27,24,28)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 248);