Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #543 |
968 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 968 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=f,c^2=f,c^a=cf,d^a=de,g^a=g^4,h^a=h^4,c^b=ce262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9364);