Finite Group DatabasebetaFinite Group Databasebeta| order | 24640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 184320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C7×C11×C16 |
| multiplicative | (ℤ/27761)ˣ, (ℤ/28589)ˣ, (ℤ/41019)ˣ, (ℤ/54692)ˣ, (ℤ/55522)ˣ, (ℤ/57178)ˣ, (ℤ/82038)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C5×C7×C11 |
| socle, prime radical | C23×C5×C7×C11 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
392 conjugacy classes of subgroups.
24640 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C23×C71 |
| outer automorphism group of | C17×C23×C71 |
Past the SmallGroups library coverage — no SmallGroups id.