Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C2×#349 |
| Sylow | C5 ⋊ D3×#349 |
| Sylow | C3 ⋊ D5×#349 |
472 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 108 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=e,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^2,e^b=eg,h^c=h^2,i^c=i^4150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38611);