Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C25×C3×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #1781 |
| Sylow | C5 ⋊ #72130 |
| Sylow | C3 ⋊ #10605024 |
1760 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 1760 conjugacy classes of subgroups — too many to draw. Only its 177 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=f,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^2,f^b=fg,i^f=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 22533);