Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#104 ⋊ C4 |
| Sylow | C5 ⋊ #10781 |
1350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^3,d^b=dh,i^b=i^2,e^c=eh,f^c=fh,i^f=i^4,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1792, #72258329, #72258376 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1792, #72258329, #72258376 |
| maximal quotient of | #72242867 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092122);