Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #10617415⋊C3 |
| Fitting | C5×#131 ⋊ C3×C4 |
| Hall | #10617415 ⋊ C3 |
| Sylow | C5 ⋊ #2875⋊C3 |
302 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^2,3,2^4,5,2|a^2=d,b^2=e,e^2=i,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, 238247);