Finite Group DatabasebetaFinite Group Databasebeta| order | 22080 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 135168 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C5×C16×C23 |
| multiplicative | (ℤ/24769)ˣ, (ℤ/25993)ˣ, (ℤ/33981)ˣ, (ℤ/35241)ˣ, (ℤ/44168)ˣ, (ℤ/44224)ˣ, (ℤ/45308)ˣ, (ℤ/46988)ˣ, (ℤ/49538)ˣ, (ℤ/51986)ˣ, (ℤ/66252)ˣ, (ℤ/67962)ˣ, (ℤ/70482)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C3×C5×C23 |
| socle, prime radical | C23×C3×C5×C23 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
392 conjugacy classes of subgroups.
22080 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C31×C47 |
| outer automorphism group of | C17×C31×C47 |
Past the SmallGroups library coverage — no SmallGroups id.