Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 21233664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C16×C81 |
| multiplicative | (ℤ/41565)ˣ, (ℤ/44336)ˣ, (ℤ/51880)ˣ, (ℤ/52160)ˣ, (ℤ/55420)ˣ, (ℤ/62256)ˣ, (ℤ/66096)ˣ, (ℤ/77760)ˣ, (ℤ/77820)ˣ, (ℤ/82620)ˣ, (ℤ/83130)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C27 | C24×C3 |
| socle, prime radical | C24×C3 | C2×C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2555 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.