Finite Group DatabasebetaFinite Group Databasebeta| order | 19680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3199795200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C25×C3×C5×C41 |
| multiplicative | (ℤ/51128)ˣ, (ℤ/61752)ˣ, (ℤ/65736)ˣ, (ℤ/76692)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2992 conjugacy classes of subgroups.
19680 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.