Finite Group DatabasebetaFinite Group Databasebeta| order | 32040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2838528 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C5×C89 |
| multiplicative | (ℤ/38843)ˣ, (ℤ/49941)ˣ, (ℤ/56091)ˣ, (ℤ/74788)ˣ, (ℤ/77686)ˣ, (ℤ/96156)ˣ, (ℤ/99882)ˣ, (ℤ/112182)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
384 conjugacy classes of subgroups.
32040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.