Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C3×C4×C5×C8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#493 |
| Sylow | C5 ⋊ D3×#493 |
| Sylow | C3 ⋊ D5×#493 |
1520 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1520 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,h^d=h^2,i^d=i^4174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 164480);