Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#468 ⋊ C2 |
| Hall | C3×C5 ⋊ #3266 |
| Sylow | C5 ⋊ #80835 |
| Sylow | C3 ⋊ #10612566 |
988 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^4,d^b=de,e^b=eg,h^b=h^2,i^b=i^4,h^c=h^2,i^c=i^4,e^d=eg,h^d=h^2,i^d=i^4141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 179424);