Finite Group DatabasebetaFinite Group Databasebeta| order | 20640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 129024 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C5×C8×C43 |
| multiplicative | (ℤ/34089)ˣ, (ℤ/36141)ˣ, (ℤ/41312)ˣ, (ℤ/45452)ˣ, (ℤ/48188)ˣ, (ℤ/61956)ˣ, (ℤ/68178)ˣ, (ℤ/72282)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C3×C5×C43 |
| socle, prime radical | C23×C3×C5×C43 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
304 conjugacy classes of subgroups.
20640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.