Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C5×C9 ⋊ #95 |
| Sylow | C9 ⋊ #3963 |
| Sylow | C5 ⋊ C9⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D9 |
| commutator | C2×C5×C9 | C42 |
| Frattini | C23×C3 | D3×D5 |
| Fitting, cosocle | C23×C5×C9 | C22 |
| socle, prime radical | C23×C3×C5 | C2×D3 |
| hypocenter | C5×C9 | #95 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C23 | |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3,5,3|a^2=e,b^2=c,f^3=h,b^a=bd,g^a=g^4,f^b=f^2h^2,h^b=h^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 72);