Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2194 |
| Sylow | C5 ⋊ #71098 |
| Sylow | C3 ⋊ #10599921 |
432 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 80 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=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,i^a=i^4,d^b=df,f^b=fg,h^b=h^2,i^b=i^4,e^c=eg135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 42237);