Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#494 ⋊ C2 |
| Hall | C3×C5 ⋊ #3293 |
| Sylow | C5 ⋊ #81808 |
| Sylow | C3 ⋊ #10613539 |
888 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 167 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=g,c^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,h^b=h^2,i^b=i^4,f^c=fg,h^c=h^2,i^c=i^4,e^d=eg,h^d=h^2,i^d=i^4183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 183927);