Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×C5×#585 ⋊ C2 |
| Hall | C3×C5 ⋊ #3027 |
| Sylow | C5 ⋊ #84126 |
| Sylow | C3 ⋊ #10615857 |
1544 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1544 conjugacy classes of subgroups — too many to draw. Only its 271 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,b^a=be,c^a=cf,d^a=dg,h^a=h^2,i^a=i^4,f^b=fg,e^c=eg267 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 151447);