Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 71663616 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C32×C9×C64 |
| multiplicative | (ℤ/25669)ˣ, (ℤ/33003)ˣ, (ℤ/36351)ˣ, (ℤ/36477)ˣ, (ℤ/51338)ˣ, (ℤ/66006)ˣ, (ℤ/72702)ˣ, (ℤ/72954)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C32 | C23×C33 |
| socle, prime radical | C23×C33 | C3×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3550 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.