Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2958824445050880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C214×C33×C4 |
| abelian | C24×C32×C42×C9 |
| multiplicative | (ℤ/69160)ˣ, (ℤ/80808)ˣ, (ℤ/82992)ˣ, (ℤ/88920)ˣ, (ℤ/93240)ˣ, (ℤ/95760)ˣ, (ℤ/98280)ˣ, (ℤ/103740)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C26×C33 |
| socle, prime radical | C26×C33 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
600750 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.