Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×C5×#496 ⋊ C2 |
| Hall | C3×C5 ⋊ #3150 |
| Sylow | C5 ⋊ #81844 |
| Sylow | C3 ⋊ #10613575 |
1128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|b^2=e,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,h^d=h^2,i^d=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 164769);