Finite Group DatabasebetaFinite Group Databasebeta| order | 22032 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11943936 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C9 |
| abelian | C22×C4×C92×C17 |
| multiplicative | (ℤ/29165)ˣ, (ℤ/34077)ˣ, (ℤ/34941)ˣ, (ℤ/41445)ˣ, (ℤ/45436)ˣ, (ℤ/46588)ˣ, (ℤ/58330)ˣ, (ℤ/66204)ˣ, (ℤ/68154)ˣ, (ℤ/69882)ˣ, (ℤ/82890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C23×C32×C17 |
| socle, prime radical | C23×C32×C17 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1242 conjugacy classes of subgroups.
22032 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.