Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C25 ⋊ #501 |
135 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=e,c^2=e,d^2=f,g^5=h,b^a=be,c^a=cd,d^a=df,g^a=g^4h^4,h^a=h^4,c^b=cef,d^c=df184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 690);