Finite Group DatabasebetaFinite Group Databasebeta| order | 3168 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10321920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C11 |
| multiplicative | (ℤ/6279)ˣ, (ℤ/6968)ˣ, (ℤ/7035)ˣ, (ℤ/7245)ˣ, (ℤ/7504)ˣ, (ℤ/8372)ˣ, (ℤ/9380)ˣ, (ℤ/9648)ˣ, (ℤ/10452)ˣ, (ℤ/10764)ˣ, (ℤ/12060)ˣ, (ℤ/12558)ˣ, (ℤ/14070)ˣ, (ℤ/14490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C11 |
| socle, prime radical | C24×C32×C11 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
3168 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.