Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 16515072 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C5×C16 |
| multiplicative | (ℤ/11067)ˣ, (ℤ/11781)ˣ, (ℤ/13496)ˣ, (ℤ/13888)ˣ, (ℤ/14756)ˣ, (ℤ/17352)ˣ, (ℤ/17856)ˣ, (ℤ/18972)ˣ, (ℤ/20244)ˣ, (ℤ/22134)ˣ, (ℤ/23562)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2640 conjugacy classes of subgroups.
5760 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.