Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #475 |
167 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=f,b^2=d,c^2=ef,e^2=f,c^a=cdef,e^a=ef,g^a=g^4,c^b=cd,g^b=g^2,h^b=h^3,g^c=h^4,h^c=g^4,g^d=g^4,h^d=h^440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5685);