Finite Group DatabasebetaFinite Group Databasebeta| order | 19488 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 516096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C7×C29 |
| multiplicative | (ℤ/22243)ˣ, (ℤ/29435)ˣ, (ℤ/30363)ˣ, (ℤ/32799)ˣ, (ℤ/36555)ˣ, (ℤ/37845)ˣ, (ℤ/38992)ˣ, (ℤ/40484)ˣ, (ℤ/43732)ˣ, (ℤ/44486)ˣ, (ℤ/48740)ˣ, (ℤ/58870)ˣ, (ℤ/60726)ˣ, (ℤ/65598)ˣ, (ℤ/73110)ˣ, (ℤ/75690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C7×C29 |
| socle, prime radical | C23×C3×C7×C29 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
19488 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.