Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#127 ⋊ C4 |
| Sylow | C5 ⋊ #10975 |
2054 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 2054 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^2,c^b=cf,d^b=dh,d^c=dh,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2002, #72221402, #72221462, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2002, #72221402, #72221462 |
| maximal quotient of | #72226453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092682);