Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C5×#331 ⋊ C2 |
| Hall | C3×C5 ⋊ #1543 |
| Sylow | C5 ⋊ #68382 |
| Sylow | C3 ⋊ #10599175 |
492 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,c^2=g,d^2=g,e^2=fg,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^c=h^2,i^c=i^4171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 10399);