Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C2×#347 |
| Sylow | C5 ⋊ D3×#347 |
| Sylow | C3 ⋊ #10603872 |
336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,i^a=i^2,d^b=dg,i^b=i^4,h^c=h^2,i^c=i^4,i^d=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38442);