Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 99090432 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43 |
| abelian | C32×C43×C5×C7 |
| multiplicative | (ℤ/22997)ˣ, (ℤ/27365)ˣ, (ℤ/45994)ˣ, (ℤ/54730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C23×C32×C5×C7 |
| socle, prime radical | C23×C32×C5×C7 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3096 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C29×C61 |
| outer automorphism group of | C13×C29×C61 |
Past the SmallGroups library coverage — no SmallGroups id.