Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ M32 |
| Sylow | C9 ⋊ #3944 |
| Sylow | C5 ⋊ #63357 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×D9 |
| commutator | C2×C5×C9 | C2×C8 |
| Frattini | C3×C8 | D3×D5 |
| Fitting, cosocle | C5×C8×C9 | C22 |
| socle | C2×C3×C5 | D3×C8 |
| prime radical | C2×C5×D9 | C8 |
| hypocenter | C5×C9 | M32 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C8 | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3,5,3|a^2=c,c^2=d,d^2=e,f^3=h,b^a=be,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, 9);