Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Sylow | C5 ⋊ C2×#2875 |
3278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,f^2=h,b^a=bh,i^a=i^2,d^c=dh,i^e=i^4,i^f=i^4176 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2875, #72242691 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2875 |
| maximal quotient of | #72242691 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114668);