Finite Group DatabasebetaFinite Group Databasebeta| order | 31104 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 83607552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C16×C81 |
| multiplicative | (ℤ/58191)ˣ, (ℤ/72632)ˣ, (ℤ/73024)ˣ, (ℤ/77588)ˣ, (ℤ/93384)ˣ, (ℤ/93888)ˣ, (ℤ/99756)ˣ, (ℤ/108864)ˣ, (ℤ/108948)ˣ, (ℤ/115668)ˣ, (ℤ/116382)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C27 | C24×C32 |
| socle, prime radical | C24×C32 | C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3960 conjugacy classes of subgroups.
31104 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.