Finite Group DatabasebetaFinite Group Databasebeta| order | 7128 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 39191040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C23×C32×C9×C11 |
| multiplicative | (ℤ/8911)ˣ, (ℤ/11457)ˣ, (ℤ/12537)ˣ, (ℤ/12663)ˣ, (ℤ/17822)ˣ, (ℤ/22914)ˣ, (ℤ/25074)ˣ, (ℤ/25326)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C33×C11 |
| socle, prime radical | C23×C33×C11 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1600 conjugacy classes of subgroups.
7128 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.