Finite Group DatabasebetaFinite Group Databasebeta| order | 19656 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1306368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C7×C9×C13 |
| multiplicative | (ℤ/30099)ˣ, (ℤ/31179)ˣ, (ℤ/40132)ˣ, (ℤ/41572)ˣ, (ℤ/59076)ˣ, (ℤ/60198)ˣ, (ℤ/62358)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C7×C13 |
| socle, prime radical | C23×C32×C7×C13 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
640 conjugacy classes of subgroups.
19656 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.