Finite Group DatabasebetaFinite Group Databasebeta| order | 19968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C13×C256 |
| multiplicative | (ℤ/20303)ˣ, (ℤ/23303)ˣ, (ℤ/29961)ˣ, (ℤ/40606)ˣ, (ℤ/46606)ˣ, (ℤ/59922)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C22×C3×C13 |
| socle, prime radical | C22×C3×C13 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
104 conjugacy classes of subgroups.
19968 conjugacy classes. The character table is too large to display.
| automorphism group of | C79×C257 |
| outer automorphism group of | C79×C257 |
Past the SmallGroups library coverage — no SmallGroups id.