Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#455 ⋊ C4 |
| Sylow | C5 ⋊ #21474 |
1422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=gh,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^3,e^b=eh,f^b=fh,d^c=dh,e^c=eh,i^d=i^2,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3019, #72222051, #72242932, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3019, #72242932, #72242941 |
| maximal quotient of | #72258314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1106463);