Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C13 ⋊ Q16 |
| Sylow | C13 ⋊ #689 |
| Sylow | C5 ⋊ #6107 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1040 |
Polycyclic presentation:
2^4,5,13|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^12,c^b=cd167 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 82);