Finite Group DatabasebetaFinite Group Databasebeta| order | 32472 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 153600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C4×C11×C41 |
| multiplicative | (ℤ/35191)ˣ, (ℤ/37891)ˣ, (ℤ/48717)ˣ, (ℤ/70382)ˣ, (ℤ/75782)ˣ, (ℤ/97434)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C32×C11×C41 |
| socle, prime radical | C22×C32×C11×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
32472 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.