Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C5×#95 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#399 |
| Sylow | C5 ⋊ D3×#399 |
| Sylow | C3 ⋊ D5×#399 |
1816 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1816 conjugacy classes of subgroups — too many to draw. Only its 268 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|a^2=e,b^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^2,h^c=h^2,h^d=h^2,i^d=i^4150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 57718);