Finite Group DatabasebetaFinite Group Databasebeta| order | 20448 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 161280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C8×C9×C71 |
| multiplicative | (ℤ/32433)ˣ, (ℤ/40904)ˣ, (ℤ/40928)ˣ, (ℤ/43244)ˣ, (ℤ/61356)ˣ, (ℤ/61452)ˣ, (ℤ/64866)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C23×C3×C71 |
| socle, prime radical | C23×C3×C71 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
228 conjugacy classes of subgroups.
20448 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.