Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×#99 |
| Sylow | C5 ⋊ Dic3×#99 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#99 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,h^a=h^2,i^a=i^3,d^b=dg,h^b=h^2,h^c=h^2,i^c=i^2,i^e=i^487 conjugacy classes — view the full character table.
| maximal subgroup of | #72229597, D3×AGL(1,𝔽5)×#99, #72230802 |
| maximal normal subgroup of | #72229597, D3×AGL(1,𝔽5)×#99, #72230802 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21110);