Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊#63419 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C5⋊#63419 |
| derived | C5×C42⋊C9 ⋊ C2 |
| Sylow | C5 ⋊ #63419 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C42⋊C9 | C2 |
| Frattini | C22×C3 | C5⋊S4 |
| Fitting | C3×C42×C5 | D3 |
| socle | C22×C3×C5 | S4 |
| LCS | G ▷ C5×C42⋊C9 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2,3,5,3,2^4|b^3=d,e^2=g,f^2=h,b^a=b^2d^2,c^a=c^4,d^a=d^2,e^a=efh,f^a=fh,g^a=gh,e^b=fg,f^b=ef,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, 258);