Finite Group DatabasebetaFinite Group Databasebeta| order | 21000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 201600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C7×C125 |
| multiplicative | (ℤ/32379)ˣ, (ℤ/36897)ˣ, (ℤ/43172)ˣ, (ℤ/49196)ˣ, (ℤ/64758)ˣ, (ℤ/73794)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C23×C3×C5×C7 |
| socle, prime radical | C23×C3×C5×C7 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
21000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.