Finite Group DatabasebetaFinite Group Databasebeta| order | 30960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1548288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C5×C43 |
| multiplicative | (ℤ/37541)ˣ, (ℤ/39221)ˣ, (ℤ/45185)ˣ, (ℤ/48267)ˣ, (ℤ/50349)ˣ, (ℤ/50427)ˣ, (ℤ/58095)ˣ, (ℤ/67132)ˣ, (ℤ/75082)ˣ, (ℤ/78442)ˣ, (ℤ/90370)ˣ, (ℤ/96534)ˣ, (ℤ/100698)ˣ, (ℤ/100854)ˣ, (ℤ/116190)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C5×C43 |
| socle, prime radical | C23×C32×C5×C43 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
30960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.