Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C3×C5×C8 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×#131 |
| Sylow | C5 ⋊ #78549 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#131 |
1144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,e^2=g,h^b=h^2,i^b=i^2,d^c=dg,h^d=h^2,i^f=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 137198);