Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ C4×H(5,𝔽2) |
| Sylow | C5 ⋊ C4×#1004 |
| Sylow | C3 ⋊ #10617787 |
3320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,i^b=i^4,i^c=i^4,h^d=h^2,i^e=i^4216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 204945);