Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 37158912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C5×C9×C16 |
| multiplicative | (ℤ/24871)ˣ, (ℤ/30039)ˣ, (ℤ/31977)ˣ, (ℤ/35343)ˣ, (ℤ/36632)ˣ, (ℤ/37696)ˣ, (ℤ/40052)ˣ, (ℤ/49742)ˣ, (ℤ/52056)ˣ, (ℤ/53568)ˣ, (ℤ/54948)ˣ, (ℤ/56916)ˣ, (ℤ/60078)ˣ, (ℤ/63954)ˣ, (ℤ/70686)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4400 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.