Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C13 ⋊ M16 |
| Sylow | C13 ⋊ #700 |
| Sylow | C5 ⋊ #6118 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 520 |
Polycyclic presentation:
2^4,5,13|a^2=c,b^2=d,c^2=d,b^a=bd,e^a=e^3,f^a=f^8,e^c=e^4,f^c=f^1274 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 128);