Finite Group DatabasebetaFinite Group Databasebeta| order | 9504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1658880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C42×C9×C11 |
| multiplicative | (ℤ/11063)ˣ, (ℤ/12395)ˣ, (ℤ/12935)ˣ, (ℤ/13895)ˣ, (ℤ/15483)ˣ, (ℤ/17865)ˣ, (ℤ/20644)ˣ, (ℤ/22126)ˣ, (ℤ/24790)ˣ, (ℤ/25870)ˣ, (ℤ/27790)ˣ, (ℤ/30966)ˣ, (ℤ/35730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
9504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.