Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C25×#104 ⋊ C2 |
| Sylow | C25 ⋊ #444 |
156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 156 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.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|c^2=d,d^2=f,e^2=f,g^5=h,b^a=be,e^a=ef,g^a=g^4h^4,h^a=h^4,c^b=ce,e^b=ef,e^c=ef190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 450);