Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6193152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C7 |
| multiplicative | (ℤ/4472)ˣ, (ℤ/4515)ˣ, (ℤ/4816)ˣ, (ℤ/5096)ˣ, (ℤ/6020)ˣ, (ℤ/6192)ˣ, (ℤ/6708)ˣ, (ℤ/7056)ˣ, (ℤ/7308)ˣ, (ℤ/7644)ˣ, (ℤ/7740)ˣ, (ℤ/8820)ˣ, (ℤ/9030)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C7 |
| socle, prime radical | C24×C32×C7 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
2016 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.