Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #10617735⋊C3 |
| Fitting | C4×C5×#41 ⋊ C2×C3 |
| Hall | #10617735 ⋊ C3 |
| Sylow | C5 ⋊ #3428⋊C3 |
730 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 111 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|b^2=i,c^2=e,f^2=i,g^2=i,c^a=ci,h^a=h^4,f^d=fg,g^d=f,g^f=gi188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239729);