Finite Group DatabasebetaFinite Group Databasebeta| order | 26136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1995840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C9×C121 |
| multiplicative | (ℤ/41439)ˣ, (ℤ/45759)ˣ, (ℤ/55252)ˣ, (ℤ/61012)ˣ, (ℤ/78444)ˣ, (ℤ/78516)ˣ, (ℤ/82878)ˣ, (ℤ/91518)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C11 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C3×C11 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
480 conjugacy classes of subgroups.
26136 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.