Finite Group DatabasebetaFinite Group Databasebeta| order | 22464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C9×C13×C16 |
| multiplicative | (ℤ/25517)ˣ, (ℤ/36261)ˣ, (ℤ/39333)ˣ, (ℤ/51034)ˣ, (ℤ/52444)ˣ, (ℤ/67428)ˣ, (ℤ/72522)ˣ, (ℤ/78666)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C32×C13 |
| socle, prime radical | C23×C32×C13 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
980 conjugacy classes of subgroups.
22464 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C19×C79 |
| outer automorphism group of | C17×C19×C79 |
Past the SmallGroups library coverage — no SmallGroups id.