Finite Group DatabasebetaFinite Group Databasebeta| order | 19080 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 209664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C9×C53 |
| multiplicative | (ℤ/22363)ˣ, (ℤ/31779)ˣ, (ℤ/44726)ˣ, (ℤ/63558)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C3×C5×C53 |
| socle, prime radical | C23×C3×C5×C53 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
19080 conjugacy classes. The character table is too large to display.
| automorphism group of | C11×C19×C107, C11×C27×C107 |
| outer automorphism group of | C11×C19×C107, C11×C27×C107 |
Past the SmallGroups library coverage — no SmallGroups id.