Finite Group DatabasebetaFinite Group Databasebeta| order | 19584 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 50734301184 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C3×C4 |
| abelian | C23×C32×C42×C17 |
| multiplicative | (ℤ/53560)ˣ, (ℤ/57680)ˣ, (ℤ/64272)ˣ, (ℤ/74160)ˣ, (ℤ/80340)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C25×C32×C17 |
| socle, prime radical | C25×C32×C17 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18000 conjugacy classes of subgroups.
19584 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.