Finite Group DatabasebetaFinite Group Databasebeta| order | 26244 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1417176 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C9 |
| abelian | C22×C9×C729 |
| multiplicative | (ℤ/27721)ˣ, (ℤ/39393)ˣ, (ℤ/41553)ˣ, (ℤ/55442)ˣ, (ℤ/78786)ˣ, (ℤ/83106)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C243 | C22×C32 |
| socle, prime radical | C22×C32 | C3×C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
375 conjugacy classes of subgroups.
26244 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1459 |
| outer automorphism group of | C19×C1459 |
Past the SmallGroups library coverage — no SmallGroups id.