Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 684913065984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C3×C43 |
| abelian | C22×C3×C43×C27 |
| multiplicative | (ℤ/56680)ˣ, (ℤ/61040)ˣ, (ℤ/68016)ˣ, (ℤ/78480)ˣ, (ℤ/84240)ˣ, (ℤ/85020)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C9 | C25×C32 |
| socle, prime radical | C25×C32 | C23×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
56658 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.