Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×C22⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C22⋊(C13×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C2×C13) |
| Fitting | C22×C5×C13 ⋊ C4 |
| Hall | C5×C13 ⋊ C22⋊C4 |
| Sylow | C5 ⋊ C13×C22⋊C4 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 260 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,18,17)(20,22);(15,16,17,18)(19,20)(21,22)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 126);