Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18579456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C5×C8×C9 |
| multiplicative | (ℤ/16359)ˣ, (ℤ/16863)ˣ, (ℤ/18104)ˣ, (ℤ/18848)ˣ, (ℤ/21812)ˣ, (ℤ/22484)ˣ, (ℤ/26784)ˣ, (ℤ/27156)ˣ, (ℤ/28044)ˣ, (ℤ/28908)ˣ, (ℤ/30996)ˣ, (ℤ/32718)ˣ, (ℤ/33726)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3380 conjugacy classes of subgroups.
8640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.