Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×D8 ⋊ C4 |
| Sylow | C5 ⋊ #12637 |
526 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 124 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=e,d^2=gh,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,c^b=ch,i^b=i^2,i^f=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2177, #72242079, #72242084, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2177, #72242079, #72242084 |
| maximal quotient of | #72242146, #72242149, #72242327 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096144);