Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2029 |
| Sylow | C5 ⋊ #68971 |
| Sylow | C3 ⋊ #10600290 |
932 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^2,i^b=i^4,h^c=h^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 34687);