Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| 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×C8×C9×C13 |
| multiplicative | (ℤ/5767)ˣ, (ℤ/5947)ˣ, (ℤ/6559)ˣ, (ℤ/8433)ˣ, (ℤ/8451)ˣ, (ℤ/11534)ˣ, (ℤ/11894)ˣ, (ℤ/13118)ˣ, (ℤ/16866)ˣ, (ℤ/16902)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C32×C13 |
| socle, prime radical | C22×C32×C13 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
220 conjugacy classes of subgroups.
5616 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.