Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9172942848 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C33×C4 |
| abelian | C22×C32×C4×C9×C16 |
| multiplicative | (ℤ/29393)ˣ, (ℤ/37791)ˣ, (ℤ/39627)ˣ, (ℤ/41769)ˣ, (ℤ/58786)ˣ, (ℤ/75582)ˣ, (ℤ/79254)ˣ, (ℤ/83538)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C8 | C24×C33 |
| socle, prime radical | C24×C33 | C2×C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
25550 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.