Finite Group DatabasebetaFinite Group Databasebeta| order | 20196 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 103680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C9×C11×C17 |
| multiplicative | (ℤ/20497)ˣ, (ℤ/20569)ˣ, (ℤ/21337)ˣ, (ℤ/30321)ˣ, (ℤ/40994)ˣ, (ℤ/41138)ˣ, (ℤ/42674)ˣ, (ℤ/60642)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C11×C17 |
| socle, prime radical | C22×C32×C11×C17 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
200 conjugacy classes of subgroups.
20196 conjugacy classes. The character table is too large to display.
| automorphism group of | C103×C199, C67×C307, C19×C1123 |
| outer automorphism group of | C103×C199, C67×C307, C19×C1123 |
Past the SmallGroups library coverage — no SmallGroups id.