Finite Group DatabasebetaFinite Group Databasebeta| order | 19920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13224960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C3×C5×C83 |
| multiplicative | (ℤ/38577)ˣ, (ℤ/41416)ˣ, (ℤ/43912)ˣ, (ℤ/51436)ˣ, (ℤ/62124)ˣ, (ℤ/65868)ˣ, (ℤ/66132)ˣ, (ℤ/77154)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
536 conjugacy classes of subgroups.
19920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.