Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C5×#97 ⋊ C4 |
| Sylow | C5 ⋊ #20451 |
1142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=ef,d^2=h,e^2=h,f^2=h,b^a=be,c^a=ch,e^b=eh,f^b=fh,i^b=i^2,i^g=i^4128 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2943, #72253211, #72269215 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2943, #72253211, #72269215 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103846);