Finite Group DatabasebetaFinite Group Databasebeta| order | 17136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 884736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C7×C17 |
| multiplicative | (ℤ/20909)ˣ, (ℤ/21749)ˣ, (ℤ/22145)ˣ, (ℤ/25235)ˣ, (ℤ/26883)ˣ, (ℤ/27963)ˣ, (ℤ/30009)ˣ, (ℤ/40012)ˣ, (ℤ/41818)ˣ, (ℤ/43498)ˣ, (ℤ/44290)ˣ, (ℤ/50470)ˣ, (ℤ/51444)ˣ, (ℤ/53766)ˣ, (ℤ/55926)ˣ, (ℤ/60018)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C7×C17 |
| socle, prime radical | C23×C32×C7×C17 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
17136 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.