Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6103 |
| Fitting | C2×C4×C5×C13 ⋊ C2 |
| Hall | C5×C13 ⋊ C22⋊C4 |
| Sylow | C13 ⋊ C5×C22⋊C4 |
68 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)(6,7,9,11,13,15,17,18,16,14,12,10,8)(19,20,21,22)(24,26);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(23,24)(25,26)290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 46);