Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1486356480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C4×C5×C7×C9 |
| multiplicative | (ℤ/48488)ˣ, (ℤ/53960)ˣ, (ℤ/55880)ˣ, (ℤ/63048)ˣ, (ℤ/64752)ˣ, (ℤ/67056)ˣ, (ℤ/68904)ˣ, (ℤ/72732)ˣ, (ℤ/75720)ˣ, (ℤ/76200)ˣ, (ℤ/76680)ˣ, (ℤ/80940)ˣ, (ℤ/83820)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C25×C3×C5×C7 |
| socle, prime radical | C25×C3×C5×C7 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8172 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.