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 ⋊ #1859 |
| Sylow | C5 ⋊ #70297 |
| Sylow | C3 ⋊ #10604003 |
604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=f,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^3,e^c=eg,i^f=i^478 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#5198, D3×#10604003, #72229797 |
| maximal normal subgroup of | AGL(1,𝔽5)×#5198, D3×#10604003, #72229797 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 25470);