Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C5 |
No aliases for this group.
| Fitting | C52×H(5,𝔽2) ⋊ C2 |
| Sylow | C52 ⋊ B(4,𝔽2) |
792 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^6,5^2|b^a=be,c^a=cd,g^a=g^4,h^a=h^4,d^b=df,e^c=ef220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5459);