Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#413 ⋊ C4 |
| Sylow | C5 ⋊ #21076 |
1022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eg,c^2=e,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 | #72221514, #72221519, AGL(1,𝔽5)×#3068, … |
| maximal normal subgroup of | #72221514, #72221519, AGL(1,𝔽5)×#3068 |
| maximal quotient of | #72223546, #72226394, #72226577 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105494);