Finite Group DatabasebetaFinite Group Databasebeta| order | 20304 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 953856 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C47 |
| multiplicative | (ℤ/26885)ˣ, (ℤ/31413)ˣ, (ℤ/35553)ˣ, (ℤ/38205)ˣ, (ℤ/41884)ˣ, (ℤ/47404)ˣ, (ℤ/53770)ˣ, (ℤ/60948)ˣ, (ℤ/62826)ˣ, (ℤ/71106)ˣ, (ℤ/76410)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32×C47 |
| socle, prime radical | C23×C32×C47 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
540 conjugacy classes of subgroups.
20304 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.