Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C5 ⋊ C8×#97 |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=cg,i^a=i^3,i^b=i^2,i^d=i^4,i^e=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1085513);