Finite Group DatabasebetaFinite Group Databasebeta| order | 19712 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1966080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C7×C8×C11×C16 |
| multiplicative | (ℤ/30171)ˣ, (ℤ/31467)ˣ, (ℤ/39488)ˣ, (ℤ/40228)ˣ, (ℤ/41956)ˣ, (ℤ/60342)ˣ, (ℤ/62934)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C23×C7×C11 |
| socle, prime radical | C23×C7×C11 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
796 conjugacy classes of subgroups.
19712 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.