Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#346 ⋊ C4 |
| Sylow | C5 ⋊ #12665 |
326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=de,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ch,d^b=dh,e^b=eh,i^b=i^2,i^f=i^4128 conjugacy classes — view the full character table.
| maximal subgroup of | #72242114, AGL(1,𝔽5)×#2171, #72242124 |
| maximal normal subgroup of | #72242114, AGL(1,𝔽5)×#2171, #72242124 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096269);