Finite Group DatabasebetaFinite Group Databasebeta| order | 31536 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 155271168 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C33×C4×C73 |
| multiplicative | (ℤ/39949)ˣ, (ℤ/51363)ˣ, (ℤ/55251)ˣ, (ℤ/79898)ˣ, (ℤ/102726)ˣ, (ℤ/110502)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C33×C73 |
| socle, prime radical | C23×C33×C73 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1512 conjugacy classes of subgroups.
31536 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.