Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 110592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C7×C9×C16 |
| multiplicative | (ℤ/22933)ˣ, (ℤ/23617)ˣ, (ℤ/23749)ˣ, (ℤ/32181)ˣ, (ℤ/32589)ˣ, (ℤ/33297)ˣ, (ℤ/33561)ˣ, (ℤ/40384)ˣ, (ℤ/42908)ˣ, (ℤ/44396)ˣ, (ℤ/45866)ˣ, (ℤ/47234)ˣ, (ℤ/47498)ˣ, (ℤ/64362)ˣ, (ℤ/65178)ˣ, (ℤ/66594)ˣ, (ℤ/67122)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C3×C5×C7 |
| socle, prime radical | C23×C3×C5×C7 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
588 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C19×C71, C17×C27×C71 |
| outer automorphism group of | C17×C19×C71, C17×C27×C71 |
Past the SmallGroups library coverage — no SmallGroups id.