Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1453 |
| Sylow | C5 ⋊ #68048 |
| Sylow | C3 ⋊ #10603863 |
380 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cg,i^a=i^3,c^b=cf,i^b=i^2,h^c=h^2,i^c=i^4,i^d=i^4,i^e=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6356);