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 ⋊ #1856 |
| Sylow | C5 ⋊ #71647 |
| Sylow | C3 ⋊ #10603925 |
648 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=f,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^3,d^b=dg,e^b=eg,i^b=i^2,d^c=dg,i^f=i^487 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#5241, #72230866, D3×#10603925 |
| maximal normal subgroup of | AGL(1,𝔽5)×#5241, #72230866, D3×#10603925 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 25306);