Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2204 |
| Sylow | C5 ⋊ #69161 |
| Sylow | C3 ⋊ #10601781 |
472 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 62 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|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cg,d^b=dg,e^b=efg,h^b=h^2,d^c=df,e^c=eg,i^c=i^4,e^d=eg87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 42690);