Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×C4⋊Q8 ⋊ C22 |
| Hall | C3×C5 ⋊ #3289 |
| Sylow | C5 ⋊ #80301 |
| Sylow | C3 ⋊ #10612032 |
896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,h^b=h^2,f^c=fg,h^c=h^2,e^d=eg,i^d=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 183580);