Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #8221 |
640 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 136 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=e,b^2=f,c^2=eg,d^2=g,b^a=bd,d^a=dg,f^a=fgh,i^a=i^4,c^b=cgh,d^b=dh,i^b=i^2,i^f=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1087323);