Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#3531⋊C5) |
| unambiguous semidirect product | #87139⋊C5 |
| Hall | #87139 ⋊ C5 |
| Sylow | C3 ⋊ #3531⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C3×#564 | C2×C5 |
| socle | C22×C3 | C2×C24⋊C5 |
| LCS | G ▷ C3×#564 | |
| UCS | C1 ◁ C22 | |
222 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2,5,2^4,3,2^2|a^2=i,c^2=i,d^2=h,e^2=hi,f^2=i,g^a=g^2,c^b=f,d^b=cf,e^b=cdf,f^b=cdef,d^c=dh,e^c=ehi,f^c=fh,e^d=ehi,f^d=fi,f^e=fi69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239377);