Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C2×C5×C4⋊Q8 ⋊ C4 |
| Sylow | C5 ⋊ #21794 |
1394 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1394 conjugacy classes of subgroups — too many to draw. Only its 224 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=g,b^2=e,d^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^2,c^b=ce,g^c=gh,i^c=i^4,i^d=i^4,i^g=i^480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1107363);