Finite Group DatabasebetaFinite Group Databasebeta| order | 20880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 129024 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C9×C29 |
| multiplicative | (ℤ/24013)ˣ, (ℤ/28025)ˣ, (ℤ/28765)ˣ, (ℤ/32037)ˣ, (ℤ/39225)ˣ, (ℤ/39825)ˣ, (ℤ/42716)ˣ, (ℤ/48026)ˣ, (ℤ/52300)ˣ, (ℤ/56050)ˣ, (ℤ/57530)ˣ, (ℤ/64074)ˣ, (ℤ/78450)ˣ, (ℤ/79650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C5×C29 |
| socle, prime radical | C23×C3×C5×C29 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
20880 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.