Finite Group DatabasebetaFinite Group Databasebeta| order | 19584 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18874368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C8×C9×C17 |
| multiplicative | (ℤ/39045)ˣ, (ℤ/40552)ˣ, (ℤ/41648)ˣ, (ℤ/49120)ˣ, (ℤ/52060)ˣ, (ℤ/58848)ˣ, (ℤ/59184)ˣ, (ℤ/60828)ˣ, (ℤ/73980)ˣ, (ℤ/78090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C24×C3×C17 |
| socle, prime radical | C24×C3×C17 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2280 conjugacy classes of subgroups.
19584 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.