Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #10619107⋊C3 |
| Fitting | C5×#577 ⋊ C2×C3 |
| Hall | #10619107 ⋊ C3 |
| Sylow | C5 ⋊ #3584⋊C3 |
668 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 77 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:
2^3,3,2^3,5,2|c^2=i,e^2=i,f^2=i,g^2=i,b^a=bi,c^a=ci,h^a=h^4,c^b=ce,e^b=ei,e^c=ei,f^d=fg,g^d=f,g^f=gi104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239866);