Finite Group DatabasebetaFinite Group Databasebeta| order | 32256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 589824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C7×C9×C64 |
| multiplicative | (ℤ/42655)ˣ, (ℤ/49839)ˣ, (ℤ/50199)ˣ, (ℤ/60615)ˣ, (ℤ/66452)ˣ, (ℤ/66932)ˣ, (ℤ/85310)ˣ, (ℤ/99678)ˣ, (ℤ/100398)ˣ, (ℤ/121230)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C32 | C23×C3×C7 |
| socle, prime radical | C23×C3×C7 | C2×C3×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
972 conjugacy classes of subgroups.
32256 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.