Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#577 ⋊ C4 |
| Sylow | C5 ⋊ #22464 |
1346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,d^b=de,e^b=eh,f^c=fh,g^c=gh,e^d=eh,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3288, #72221478, #72221480, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3288, #72221478, #72221480 |
| maximal quotient of | #72223094, #72223394, #72223445 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1109813);