Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C22×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #13851 |
4614 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 432 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=h,d^2=g,b^a=be,c^a=cf,i^a=i^2,c^b=cg,i^h=i^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098346);