Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C212 |
No aliases for this group.
| Fitting | C26×C5 ⋊ C4 |
| Sylow | C5 ⋊ #14679 |
30862 conjugacy classes of subgroups; only the 816 normal subgroups are shown.
This group has 30862 conjugacy classes of subgroups — too many to draw. Only its 816 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=h,b^a=be,c^a=cf,d^a=dg,i^a=i^2,i^h=i^4152 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2846, #72242752, #72242753, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2846, #72242752, #72242753, … |
| maximal quotient of | #72242757 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1099174);