Finite Group DatabasebetaFinite Group Databasebeta| order | 19440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 124416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C243 |
| multiplicative | (ℤ/26785)ˣ, (ℤ/36525)ˣ, (ℤ/38888)ˣ, (ℤ/40095)ˣ, (ℤ/48700)ˣ, (ℤ/53570)ˣ, (ℤ/58332)ˣ, (ℤ/72900)ˣ, (ℤ/73050)ˣ, (ℤ/80190)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C81 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C2×C81 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
19440 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.