Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C5×B(4,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #21482 |
1630 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 214 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=gh,b^a=be,c^a=cf,d^a=dh,i^a=i^3,f^b=fh,e^c=eh,i^d=i^2,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3027, AGL(1,𝔽5)×#3026, #72242930, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3027, AGL(1,𝔽5)×#3026, #72242930, … |
| maximal quotient of | #72242721 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1106477);