Finite Group DatabasebetaFinite Group Databasebeta| order | 18720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 110592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C8×C9×C13 |
| multiplicative | (ℤ/28689)ˣ, (ℤ/29697)ˣ, (ℤ/30921)ˣ, (ℤ/37472)ˣ, (ℤ/38252)ˣ, (ℤ/39596)ˣ, (ℤ/41228)ˣ, (ℤ/56268)ˣ, (ℤ/57378)ˣ, (ℤ/59394)ˣ, (ℤ/61842)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C23×C3×C5×C13 |
| socle, prime radical | C23×C3×C5×C13 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
456 conjugacy classes of subgroups.
18720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.