Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 147456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C7×C256 |
| multiplicative | (ℤ/33153)ˣ, (ℤ/37779)ˣ, (ℤ/44032)ˣ, (ℤ/44204)ˣ, (ℤ/50176)ˣ, (ℤ/50372)ˣ, (ℤ/66306)ˣ, (ℤ/75558)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C23×C3×C7 |
| socle, prime radical | C23×C3×C7 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
372 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.