Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D5⋊C8 |
| unambiguous semidirect product | D5⋊(C8×C13) |
| derived, Sylow | C5 ⋊ C2×C8×C13 |
| Hall | C5×C13 ⋊ C2×C8 |
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)(14,15,16,18,17)(19,21,23,22)(20,24,26,25);(15,16,17,18)(19,20,22,25,23,26,21,24)260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 120);