Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of (C22⋊C9)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C22⋊C9)⋊#170 |
| derived | C5×C22⋊C9 ⋊ C8 |
| Sylow | C5 ⋊ (C22⋊C9)⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C22⋊C9)⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C22⋊C9 | C8 |
| Frattini | C2×C3 | A4⋊AGL(1,𝔽5) |
| Fitting, socle, prime radical | C23×C3×C5 | Dic3 |
| cosocle | Dic5×C22⋊C9 | C2 |
| LCS | G ▷ C5×C22⋊C9 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^3,3,5,3,2^2|a^2=b,b^2=c,d^3=f,d^a=d^2f^2,e^a=e^2,f^a=f^2,g^a=gh,e^b=e^4,g^d=h,h^d=gh60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1459);