Finite Group DatabasebetaFinite Group Databasebeta| order | 20640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 516096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C5×C43 |
| multiplicative | (ℤ/24739)ˣ, (ℤ/26815)ˣ, (ℤ/28015)ˣ, (ℤ/30275)ˣ, (ℤ/31659)ˣ, (ℤ/38925)ˣ, (ℤ/42212)ˣ, (ℤ/49478)ˣ, (ℤ/53630)ˣ, (ℤ/56030)ˣ, (ℤ/60550)ˣ, (ℤ/63318)ˣ, (ℤ/77850)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C5×C43 |
| socle, prime radical | C23×C3×C5×C43 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
20640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.