Finite Group DatabasebetaFinite Group Databasebeta| order | 20304 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 79488 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C8×C9×C47 |
| multiplicative | (ℤ/20659)ˣ, (ℤ/21451)ˣ, (ℤ/30483)ˣ, (ℤ/41318)ˣ, (ℤ/42902)ˣ, (ℤ/60966)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C32×C47 |
| socle, prime radical | C22×C32×C47 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
220 conjugacy classes of subgroups.
20304 conjugacy classes. The character table is too large to display.
| automorphism group of | C73×C283, C19×C1129 |
| outer automorphism group of | C73×C283, C19×C1129 |
Past the SmallGroups library coverage — no SmallGroups id.