Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×#97 |
| Sylow | C5 ⋊ Dic3×#97 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#97 |
720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bg,h^a=h^2,h^c=h^2,i^c=i^2,i^f=i^4156 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#97 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 19925);