Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2148 |
| Sylow | C5 ⋊ #69266 |
| Sylow | C3 ⋊ #10604859 |
440 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 440 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=e,c^2=g,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,i^a=i^2,d^b=dfg,e^b=eg,f^b=fg,h^b=h^2,h^c=h^2,i^e=i^469 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 39985);