Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×C4⋊C8 |
| Sylow | C5 ⋊ #68602 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×C4⋊C8 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,i^a=i^2,h^c=h^2,i^c=i^3,i^e=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21825);