Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1406 |
| Sylow | C5 ⋊ #67797 |
| Sylow | C3 ⋊ #10598035 |
216 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=d,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,i^b=i^4,d^c=dfg,e^d=eg84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5097);