Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C25×H(5,𝔽2) ⋊ C2 |
| Sylow | C25 ⋊ B(4,𝔽2) |
297 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 59 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|g^5=h,b^a=be,c^a=cd,g^a=g^4h^4,h^a=h^4,d^b=df,e^c=ef220 conjugacy classes — view the full character table.
| maximal subgroup of | D25×B(4,𝔽2), #72275792 |
| maximal normal subgroup of | D25×B(4,𝔽2), #72275792 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 871);