Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊(C5⋊#857) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊(C5⋊#857) |
| unambiguous semidirect product | C5⋊(C3⋊#857) |
| Fitting | C3×C42×C5 ⋊ D3 |
| derived | C3×C5×C42⋊C3 ⋊ C2 |
| Sylow | C5 ⋊ C3⋊#857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×C42⋊C3 | C2 |
| Frattini | C22 | C3⋊(C5⋊S4) |
| Fitting | C3×C42×C5 | D3 |
| socle | C22×C3×C5 | S4 |
| LCS | G ▷ C3×C5×C42⋊C3 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2,3^2,5,2^4|e^2=g,f^2=h,b^a=b^2,c^a=c^2,d^a=d^4,e^a=ef,f^a=fh,g^a=gh,e^b=fgh,f^b=efg,g^b=h,h^b=gh66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2533);