Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8626176 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C33×C4×C5 |
| multiplicative | (ℤ/2821)ˣ, (ℤ/3627)ˣ, (ℤ/3843)ˣ, (ℤ/5642)ˣ, (ℤ/7254)ˣ, (ℤ/7686)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C33×C5 |
| socle, prime radical | C23×C33×C5 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1512 conjugacy classes of subgroups.
2160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.