Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C3×C42×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #2285 |
| Sylow | C5 ⋊ #82062 |
| Sylow | C3 ⋊ #10617048 |
1312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^2,i^a=i^2,i^g=i^4216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45861);