Finite Group DatabasebetaFinite Group Databasebeta| order | 19008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 829440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C9×C11×C16 |
| multiplicative | (ℤ/21641)ˣ, (ℤ/23681)ˣ, (ℤ/30447)ˣ, (ℤ/30753)ˣ, (ℤ/43282)ˣ, (ℤ/47362)ˣ, (ℤ/60894)ˣ, (ℤ/61506)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
980 conjugacy classes of subgroups.
19008 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C19×C67, C17×C27×C67 |
| outer automorphism group of | C17×C19×C67, C17×C27×C67 |
Past the SmallGroups library coverage — no SmallGroups id.