Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of #6095 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D104 |
| Fitting | C5×C8×C13 ⋊ C2 |
| Hall | C5×C13 ⋊ D8 |
| Sylow | C13 ⋊ C5×D8 |
44 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)(14,15,16,17,18,19,20,21,22,23,24,25,26);(7,13)(8,12)(9,11)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 39);