Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C7×#3930 |
| Fitting | C5×C7×C16 ⋊ C2 |
| 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)(8,9,11,12,10)(13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28);(9,10)(11,12)(14,18)(19,24)(20,25)(26,28)364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 116);