Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #350 |
174 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=cdef,c^2=f,d^2=e,e^2=f,b^a=bc,h^a=h^4,c^b=cf,d^b=df,g^b=g^4196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1635);