Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C5×C9 ⋊ C2×C16 |
| Sylow | C9 ⋊ D5×C16 |
| Sylow | C5 ⋊ C16×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×D9 |
| commutator, hypocenter | C5×C9 | C2×C16 |
| Frattini | C3×C8 | D3×D5 |
| Fitting, cosocle | C5×C8×C9 | C22 |
| socle | C2×C3×C5 | D3×C8 |
| prime radical | C2×D45 | C8 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C8 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3,5,3|a^2=c,b^2=c,c^2=d,d^2=e,f^3=h,g^a=g^4,f^b=f^2h^2,h^b=h^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 8);