Finite Group DatabasebetaFinite Group Databasebeta| order | 19440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 78382080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C3×C5×C81 |
| multiplicative | (ℤ/37653)ˣ, (ℤ/40424)ˣ, (ℤ/45416)ˣ, (ℤ/50204)ˣ, (ℤ/58392)ˣ, (ℤ/60264)ˣ, (ℤ/60636)ˣ, (ℤ/64548)ˣ, (ℤ/68124)ˣ, (ℤ/74844)ˣ, (ℤ/75306)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2412 conjugacy classes of subgroups.
19440 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.