Finite Group DatabasebetaFinite Group Databasebeta| order | 20856 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C11×C79 |
| multiplicative | (ℤ/21239)ˣ, (ℤ/31287)ˣ, (ℤ/41716)ˣ, (ℤ/42478)ˣ, (ℤ/62574)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C11×C79 |
| socle, prime radical | C22×C3×C11×C79 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
20856 conjugacy classes. The character table is too large to display.
| automorphism group of | C67×C317 |
| outer automorphism group of | C67×C317 |
Past the SmallGroups library coverage — no SmallGroups id.