Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1614 |
| Sylow | C5 ⋊ #68322 |
| Sylow | C3 ⋊ #10598910 |
472 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=fg,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^2,i^a=i^4,d^b=df,e^b=eg,h^b=h^2,i^b=i^4,d^c=dg,h^c=h^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 14291);