Finite Group DatabasebetaFinite Group Databasebeta| order | 5940 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 25920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C5×C9×C11 |
| multiplicative | (ℤ/6169)ˣ, (ℤ/6289)ˣ, (ℤ/6937)ˣ, (ℤ/8919)ˣ, (ℤ/8937)ˣ, (ℤ/12338)ˣ, (ℤ/12578)ˣ, (ℤ/13874)ˣ, (ℤ/17838)ˣ, (ℤ/17874)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C5×C11 |
| socle, prime radical | C22×C32×C5×C11 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
200 conjugacy classes of subgroups.
5940 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.