Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C5×#99 ⋊ C4 |
| Sylow | C5 ⋊ #10938 |
1234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^3,d^b=dh,e^b=eh,f^b=fh,d^c=dh,i^c=i^2,i^f=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | #72221753, AGL(1,𝔽5)×#1913, #72242869, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1913, #72242869, #72243039, … |
| maximal quotient of | #72221753 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092585);