Finite Group DatabasebetaFinite Group Databasebeta| order | 19728 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 156672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C9×C137 |
| multiplicative | (ℤ/37005)ˣ, (ℤ/39464)ˣ, (ℤ/39472)ˣ, (ℤ/49340)ˣ, (ℤ/59196)ˣ, (ℤ/74010)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C137 |
| socle, prime radical | C23×C3×C137 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
162 conjugacy classes of subgroups.
19728 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.