Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | H(7,𝔽2) ⋊ D5 |
643 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 643 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
2,5,2^7|d^2=i,e^2=i,g^2=i,h^2=i,b^a=b^4,c^a=cdef,d^a=df,e^a=efi,g^a=gh,h^a=hi,c^b=ce,d^b=dfi,e^b=cef,f^b=cd,d^c=di,e^c=ei,f^c=fi,e^d=ei,h^g=hi32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116423);