Finite Group DatabasebetaFinite Group Databasebeta| order | 32256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1090990412660736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C212×C3×C43 |
| abelian | C23×C32×C43×C7 |
| multiplicative | (ℤ/105560)ˣ, (ℤ/126672)ˣ, (ℤ/134160)ˣ, (ℤ/135720)ˣ, (ℤ/146160)ˣ, (ℤ/152880)ˣ, (ℤ/158340)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C26×C32×C7 |
| socle, prime radical | C26×C32×C7 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
406296 conjugacy classes of subgroups.
32256 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.