Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C5×#100 ⋊ C4 |
| Sylow | C5 ⋊ #21078 |
1118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=egh,c^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^3,d^b=dh,i^b=i^2,f^c=fh,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | #72221508, #72221514, AGL(1,𝔽5)×#3068, … |
| maximal normal subgroup of | #72221508, #72221514, AGL(1,𝔽5)×#3068 |
| maximal quotient of | #72223537, #72226396, #72226569 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105496);