Finite Group DatabasebetaFinite Group Databasebeta| order | 21060 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 15552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C5×C13×C81 |
| multiplicative | (ℤ/21353)ˣ, (ℤ/31593)ˣ, (ℤ/31833)ˣ, (ℤ/42124)ˣ, (ℤ/42706)ˣ, (ℤ/63186)ˣ, (ℤ/63666)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
100 conjugacy classes of subgroups.
21060 conjugacy classes. The character table is too large to display.
| automorphism group of | C131×C163 |
| outer automorphism group of | C131×C163 |
Past the SmallGroups library coverage — no SmallGroups id.