Finite Group DatabasebetaFinite Group Databasebeta| order | 18792 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 254016 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C29×C81 |
| multiplicative | (ℤ/28851)ˣ, (ℤ/38468)ˣ, (ℤ/57348)ˣ, (ℤ/57702)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C23×C3×C29 |
| socle, prime radical | C23×C3×C29 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
160 conjugacy classes of subgroups.
18792 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.