Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#3926) |
| Hall | C3×C5 ⋊ C4⋊C32 |
| Sylow | C5 ⋊ C4⋊(C3⋊C32) |
| Sylow | C3 ⋊ C4⋊#3926 |
124 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^2,i^a=i^4528 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5386);