Finite Group DatabasebetaFinite Group Databasebeta| order | 22704 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 161280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C11×C43 |
| multiplicative | (ℤ/27853)ˣ, (ℤ/33145)ˣ, (ℤ/34773)ˣ, (ℤ/35811)ˣ, (ℤ/36933)ˣ, (ℤ/42615)ˣ, (ℤ/46364)ˣ, (ℤ/49244)ˣ, (ℤ/55706)ˣ, (ℤ/66290)ˣ, (ℤ/69546)ˣ, (ℤ/71622)ˣ, (ℤ/73866)ˣ, (ℤ/85230)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C11×C43 |
| socle, prime radical | C23×C3×C11×C43 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
22704 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.