Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×#108 ⋊ C2 |
| Sylow | C52 ⋊ #472 |
432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 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|b^2=ef,c^2=e,d^2=f,e^2=f,b^a=be,c^a=cef,e^a=ef,g^a=g^4,h^a=h^4,c^b=cd,d^b=df,d^c=df184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5113);