Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 20736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C7×C9×C16 |
| multiplicative | (ℤ/6403)ˣ, (ℤ/7063)ˣ, (ℤ/9081)ˣ, (ℤ/9099)ˣ, (ℤ/12806)ˣ, (ℤ/14126)ˣ, (ℤ/18162)ˣ, (ℤ/18198)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C22×C32×C7 |
| socle, prime radical | C22×C32×C7 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
280 conjugacy classes of subgroups.
6048 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.