Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #430 |
272 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 66 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=d,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^3,h^a=h^2,c^b=cf,g^d=g^4,h^d=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #72221123, #72223072 |
| maximal normal subgroup of | #72221123, #72223072 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7219);