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 ⋊ #1827 |
| Sylow | C5 ⋊ #70131 |
| Sylow | C3 ⋊ #10604158 |
524 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 102 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,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^2,f^b=fg,f^c=fg,h^c=h^2,i^f=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 24318);