Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #327 |
274 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 52 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=ef,b^a=bc,c^a=ce,h^a=h^4,c^b=cf,d^b=df,g^b=g^4163 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1673);