Finite Group DatabasebetaFinite Group Databasebeta| order | 31968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8695185408 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33 |
| abelian | C23×C33×C4×C37 |
| multiplicative | (ℤ/60879)ˣ, (ℤ/70245)ˣ, (ℤ/81172)ˣ, (ℤ/104364)ˣ, (ℤ/121758)ˣ, (ℤ/140490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C33×C37 |
| socle, prime radical | C24×C33×C37 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6608 conjugacy classes of subgroups.
31968 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.