Finite Group DatabasebetaFinite Group Databasebeta| order | 20000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 215040000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C5 |
| abelian | C23×C4×C5×C125 |
| multiplicative | (ℤ/41415)ˣ, (ℤ/44176)ˣ, (ℤ/50200)ˣ, (ℤ/55000)ˣ, (ℤ/55220)ˣ, (ℤ/75300)ˣ, (ℤ/82500)ˣ, (ℤ/82830)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C25 | C24×C52 |
| socle, prime radical | C24×C52 | C2×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2360 conjugacy classes of subgroups.
20000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.