Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 66060288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C5×C64 |
| multiplicative | (ℤ/44583)ˣ, (ℤ/47864)ˣ, (ℤ/55552)ˣ, (ℤ/59444)ˣ, (ℤ/71424)ˣ, (ℤ/71796)ˣ, (ℤ/76428)ˣ, (ℤ/89166)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3864 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.