Finite Group DatabasebetaFinite Group Databasebeta| order | 29568 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10321920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C7×C11×C16 |
| multiplicative | (ℤ/50439)ˣ, (ℤ/54579)ˣ, (ℤ/57477)ˣ, (ℤ/60568)ˣ, (ℤ/62008)ˣ, (ℤ/62968)ˣ, (ℤ/63296)ˣ, (ℤ/67252)ˣ, (ℤ/72128)ˣ, (ℤ/72772)ˣ, (ℤ/76636)ˣ, (ℤ/88728)ˣ, (ℤ/88896)ˣ, (ℤ/90852)ˣ, (ℤ/93012)ˣ, (ℤ/93564)ˣ, (ℤ/94452)ˣ, (ℤ/100878)ˣ, (ℤ/109158)ˣ, (ℤ/114954)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C24×C3×C7×C11 |
| socle, prime radical | C24×C3×C7×C11 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1760 conjugacy classes of subgroups.
29568 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.