Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C5×H(5,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #20609 |
4122 conjugacy classes of subgroups; only the 358 normal subgroups are shown.
This group has 4122 conjugacy classes of subgroups — too many to draw. Only its 358 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,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^2,f^b=fh,g^b=gh,e^c=eh,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3026, #72242869, #72242874, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3026, #72242869, #72242874, … |
| maximal quotient of | #72242757 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104459);