Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C4×C5×Q8 ⋊ C4 |
| Hall | C3×C5 ⋊ #1805 |
| Sylow | C5 ⋊ #71627 |
| Sylow | C3 ⋊ #10604452 |
584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=dg,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,i^a=i^2,e^c=eg,i^f=i^4138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 23473);