Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#95 ⋊ C4 |
| Hall | C3×C5 ⋊ #1443 |
| Sylow | C5 ⋊ #69416 |
| Sylow | C3 ⋊ #10603803 |
952 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 221 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=g,b^2=de,c^2=d,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,c^b=cf,i^g=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5916);