Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#704 |
| Hall | C5×C13 ⋊ M16 |
| Sylow | C5 ⋊ C13×M16 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 520 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,18,17)(20,23)(24,26);(15,16,17,18)(19,20,21,24,22,23,25,26)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 125);