Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#322 ⋊ C4 |
| Sylow | C5 ⋊ #8284 |
430 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=de,d^2=g,e^2=h,b^a=bd,c^a=cg,d^b=dg,e^b=eg,i^b=i^2,i^f=i^4128 conjugacy classes — view the full character table.
| maximal subgroup of | #72242073, AGL(1,𝔽5)×#1580, #72242079, … |
| maximal normal subgroup of | #72242073, AGL(1,𝔽5)×#1580, #72242079 |
| maximal quotient of | #72242073, #72242114, #72253135 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1087602);