Finite Group DatabasebetaFinite Group Databasebeta| order | 19680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C5×C16×C41 |
| multiplicative | (ℤ/20003)ˣ, (ℤ/20927)ˣ, (ℤ/40006)ˣ, (ℤ/41854)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C3×C5×C41 |
| socle, prime radical | C22×C3×C5×C41 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
112 conjugacy classes of subgroups.
19680 conjugacy classes. The character table is too large to display.
| automorphism group of | C83×C241, C17×C1231 |
| outer automorphism group of | C83×C241, C17×C1231 |
Past the SmallGroups library coverage — no SmallGroups id.