Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 49313740750848 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C33×C43 |
| abelian | C22×C32×C43×C9 |
| multiplicative | (ℤ/50505)ˣ, (ℤ/53872)ˣ, (ℤ/67340)ˣ, (ℤ/69264)ˣ, (ℤ/86580)ˣ, (ℤ/101010)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C3 | C25×C33 |
| socle, prime radical | C25×C33 | C23×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
202350 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.