Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ M32 |
| Sylow | C32 ⋊ #3930 |
| Sylow | C5 ⋊ #63625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D5×C3⋊D3 |
| commutator, socle | C2×C32×C5 | C2×C8 |
| Fitting, cosocle | C32×C5×C8 | C22 |
| prime radical | C2×C3⋊D15 | C8 |
| hypocenter | C32×C5 | M32 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=c,c^2=d,d^2=e,b^a=be,h^a=h^4,f^b=f^2,g^b=g^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1021);