Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×#349 ⋊ C2 |
| Hall | C3×C5 ⋊ #2238 |
| Sylow | C5 ⋊ #69116 |
| Sylow | C3 ⋊ #10599909 |
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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|c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,i^a=i^4,e^b=eg,d^c=dg,e^c=efg,f^c=fg,h^c=h^2,i^c=i^4174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 44223);