Finite Group DatabasebetaFinite Group Databasebeta| order | 19680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 122880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C5×C8×C41 |
| multiplicative | (ℤ/23821)ˣ, (ℤ/30627)ˣ, (ℤ/35301)ˣ, (ℤ/39392)ˣ, (ℤ/47068)ˣ, (ℤ/47642)ˣ, (ℤ/60516)ˣ, (ℤ/61254)ˣ, (ℤ/70602)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C3×C5×C41 |
| socle, prime radical | C23×C3×C5×C41 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
304 conjugacy classes of subgroups.
19680 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.