Finite Group DatabasebetaFinite Group Databasebeta| order | 20400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 122880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C17×C25 |
| multiplicative | (ℤ/31209)ˣ, (ℤ/38265)ˣ, (ℤ/38625)ˣ, (ℤ/40808)ˣ, (ℤ/40816)ˣ, (ℤ/41612)ˣ, (ℤ/51020)ˣ, (ℤ/51500)ˣ, (ℤ/61212)ˣ, (ℤ/62418)ˣ, (ℤ/76530)ˣ, (ℤ/77250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C23×C3×C5×C17 |
| socle, prime radical | C23×C3×C5×C17 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
20400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.