Finite Group DatabasebetaFinite Group Databasebeta| order | 18000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 921600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C125 |
| multiplicative | (ℤ/22841)ˣ, (ℤ/26285)ˣ, (ℤ/29289)ˣ, (ℤ/29367)ˣ, (ℤ/33795)ˣ, (ℤ/39052)ˣ, (ℤ/39375)ˣ, (ℤ/45682)ˣ, (ℤ/52570)ˣ, (ℤ/58578)ˣ, (ℤ/58734)ˣ, (ℤ/67590)ˣ, (ℤ/78750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C25 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
18000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.