Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | Q8⋊#6034 |
| Sylow | C52 ⋊ Q8⋊C8 |
210 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=e,c^2=f,d^2=e,b^a=bd,d^a=de,g^a=g^3,h^a=h^2,d^b=de,g^c=g^4,h^c=h^488 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2752);