Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#413 ⋊ C4 |
| Sylow | C5 ⋊ #10755 |
1210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,g^2=h,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,i^b=i^2,d^c=dh,i^f=i^4,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1914, #72221471, #72221475, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1914, #72221471, #72221475 |
| maximal quotient of | #72221719, #72226470 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092044);