Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #34200 |
3534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=h,d^2=f,b^a=bf,c^a=cg,e^a=ef,i^a=i^4,d^b=df248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 329850);