Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1397 |
| Sylow | C5 ⋊ #67589 |
| Sylow | C3 ⋊ #10598080 |
136 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 83 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=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^2,i^b=i^4528 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4899);