Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 49545216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C5×C7×C8 |
| multiplicative | (ℤ/37023)ˣ, (ℤ/42656)ˣ, (ℤ/47264)ˣ, (ℤ/48608)ˣ, (ℤ/49364)ˣ, (ℤ/60768)ˣ, (ℤ/63468)ˣ, (ℤ/70812)ˣ, (ℤ/72324)ˣ, (ℤ/74046)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C32×C5×C7 |
| socle, prime radical | C24×C32×C5×C7 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4056 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.