Finite Group DatabasebetaFinite Group Databasebeta| order | 19656 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 62208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C7×C9×C13 |
| multiplicative | (ℤ/19939)ˣ, (ℤ/20239)ˣ, (ℤ/20767)ˣ, (ℤ/21463)ˣ, (ℤ/29511)ˣ, (ℤ/39878)ˣ, (ℤ/40478)ˣ, (ℤ/41534)ˣ, (ℤ/42926)ˣ, (ℤ/59022)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C7×C13 |
| socle, prime radical | C22×C32×C7×C13 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
19656 conjugacy classes. The character table is too large to display.
| automorphism group of | C127×C157, C37×C547, C19×C1093 |
| outer automorphism group of | C127×C157, C37×C547, C19×C1093 |
Past the SmallGroups library coverage — no SmallGroups id.