Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10617199⋊C3 |
| Hall | #10617199 ⋊ C3 |
| Sylow | C5 ⋊ #2982⋊C3 |
252 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 50 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:
2^2,3,2^4,5,2|a^2=d,b^2=e,d^2=e,f^2=i,g^2=i,b^a=bi,h^a=h^2,f^c=fg,g^c=f,h^d=h^4,g^f=gi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238220);