Finite Group DatabasebetaFinite Group Databasebeta| order | 22464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1391229665280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C33 |
| abelian | C24×C33×C4×C13 |
| multiplicative | (ℤ/57512)ˣ, (ℤ/73944)ˣ, (ℤ/79128)ˣ, (ℤ/79632)ˣ, (ℤ/85176)ˣ, (ℤ/86268)ˣ, (ℤ/99540)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C33×C13 |
| socle, prime radical | C25×C33×C13 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
38136 conjugacy classes of subgroups.
22464 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.