Finite Group DatabasebetaFinite Group Databasebeta| order | 20088 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 933120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C9 |
| abelian | C2×C4×C92×C31 |
| multiplicative | (ℤ/21223)ˣ, (ℤ/30159)ˣ, (ℤ/42446)ˣ, (ℤ/60318)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C22×C32×C31 |
| socle, prime radical | C22×C32×C31 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
368 conjugacy classes of subgroups.
20088 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1117 |
| outer automorphism group of | C19×C1117 |
Past the SmallGroups library coverage — no SmallGroups id.