Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#685 |
| Fitting | C2×C4×C5×C13 ⋊ C2 |
| Hall | C5×C13 ⋊ C22⋊C4 |
| Sylow | C5 ⋊ C13×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:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,18,16)(19,20,21,22)(24,26);(15,16)(17,18)(23,24)(25,26)338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 62);