Finite Group DatabasebetaFinite Group Databasebeta| order | 32256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 695784701952 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C3×C43 |
| abelian | C22×C32×C42×C7×C8 |
| multiplicative | (ℤ/84448)ˣ, (ℤ/89440)ˣ, (ℤ/101920)ˣ, (ℤ/108576)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4 | C25×C32×C7 |
| socle, prime radical | C25×C32×C7 | C22×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
79128 conjugacy classes of subgroups.
32256 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.