Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8709120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C3×C5×C9 |
| multiplicative | (ℤ/4389)ˣ, (ℤ/4712)ˣ, (ℤ/5852)ˣ, (ℤ/6696)ˣ, (ℤ/7068)ˣ, (ℤ/7524)ˣ, (ℤ/8316)ˣ, (ℤ/8778)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1340 conjugacy classes of subgroups.
2160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.