Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C5×#131 ⋊ C4 |
| Sylow | C5 ⋊ #20663 |
1438 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eh,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,d^c=dh,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3058, #72242588 |
| maximal normal subgroup of | AGL(1,𝔽5)×#3058 |
| maximal quotient of | #72242588 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104577);