Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C25×C4 ⋊ D5 |
1447 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 1447 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2,5,2^7|g^2=h,b^a=b^4,c^a=cdef,d^a=df,e^a=ef,g^a=gi,c^b=ce,d^b=df,e^b=cef,f^b=cd56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116387);