Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C4×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #1414 |
| Sylow | C5 ⋊ #67782 |
| Sylow | C3 ⋊ #10598519 |
168 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,i^a=i^3,c^b=cfg,d^b=defg,e^b=eg,i^b=i^4,d^c=dfg,e^d=eg,i^d=i^4135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5244);