Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C5×#127 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#453 |
| Sylow | C5 ⋊ D3×#453 |
| Sylow | C3 ⋊ D5×#453 |
1688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,f^b=fg,h^b=h^2,e^c=eg,h^d=h^2,i^d=i^4108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×#453 |
| maximal normal subgroup of | D3×D5×#453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 150677);