Finite Group DatabasebetaFinite Group Databasebeta| order | 22440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 215040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C11×C17 |
| multiplicative | (ℤ/26059)ˣ, (ℤ/37059)ˣ, (ℤ/37389)ˣ, (ℤ/39291)ˣ, (ℤ/49412)ˣ, (ℤ/49852)ˣ, (ℤ/52118)ˣ, (ℤ/52388)ˣ, (ℤ/67356)ˣ, (ℤ/74118)ˣ, (ℤ/74778)ˣ, (ℤ/78582)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
22440 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.