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×C4⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ #2274 |
| Sylow | C5 ⋊ #82144 |
| Sylow | C3 ⋊ #10617098 |
1392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,h^a=h^2,i^a=i^2,c^b=ce,i^f=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45373);