Finite Group DatabasebetaFinite Group Databasebeta| order | 17760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6193152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C5×C37 |
| multiplicative | (ℤ/34419)ˣ, (ℤ/36795)ˣ, (ℤ/36952)ˣ, (ℤ/39248)ˣ, (ℤ/44600)ˣ, (ℤ/45892)ˣ, (ℤ/49060)ˣ, (ℤ/53304)ˣ, (ℤ/55428)ˣ, (ℤ/59004)ˣ, (ℤ/66900)ˣ, (ℤ/68838)ˣ, (ℤ/73590)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C5×C37 |
| socle, prime radical | C24×C3×C5×C37 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
17760 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.