Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×#101 |
| Sylow | C5 ⋊ #68973 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#101 |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=eg,f^2=g,b^a=bd,f^a=fg,i^a=i^2,d^b=dg,h^c=h^2,i^c=i^3,i^e=i^487 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21193);