Finite Group DatabasebetaFinite Group Databasebeta| order | 32016 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 236544 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C23×C29 |
| multiplicative | (ℤ/36049)ˣ, (ℤ/41005)ˣ, (ℤ/49029)ˣ, (ℤ/49209)ˣ, (ℤ/60045)ˣ, (ℤ/64048)ˣ, (ℤ/65372)ˣ, (ℤ/65612)ˣ, (ℤ/72098)ˣ, (ℤ/80060)ˣ, (ℤ/82010)ˣ, (ℤ/98058)ˣ, (ℤ/98418)ˣ, (ℤ/120090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C23×C29 |
| socle, prime radical | C23×C3×C23×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
32016 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.