Finite Group DatabasebetaFinite Group Databasebeta| order | 19008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 138240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C11×C16×C27 |
| multiplicative | (ℤ/29877)ˣ, (ℤ/31671)ˣ, (ℤ/39836)ˣ, (ℤ/59754)ˣ, (ℤ/63342)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C9 | C23×C3×C11 |
| socle, prime radical | C23×C3×C11 | C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
392 conjugacy classes of subgroups.
19008 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C23×C81 |
| outer automorphism group of | C17×C23×C81 |
Past the SmallGroups library coverage — no SmallGroups id.