Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic65 |
| Hall | C5×C13 ⋊ C4⋊C4 |
| Sylow | C13 ⋊ C4⋊Dic5 |
| Sylow | C5 ⋊ C4⋊Dic13 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1040 |
Polycyclic presentation:
2^4,5,13|a^2=d,b^2=c,b^a=bc,e^a=e^4,f^a=f^12266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 77);