Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#3926 |
| Hall | C3×C5 ⋊ C22⋊C32 |
| Sylow | C5 ⋊ (C2×D3)⋊C32 |
| Sylow | C3 ⋊ C22⋊#3926 |
164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,i^a=i^4,h^b=h^2336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4951);