Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Fitting | C4×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #20331 |
1470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=g,e^2=h,c^a=ch,i^a=i^3,d^b=dh,i^b=i^2,i^e=i^4,i^f=i^4176 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2875, #72242692, #72269233 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2875, #72269233 |
| maximal quotient of | #72242692 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103390);