Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #20824 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=f,d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^2,c^b=ch,d^c=dh,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3184, #72221440, #72221445, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3184, #72221440, #72221445, … |
| maximal quotient of | #72223096 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104976);