Finite Group DatabasebetaFinite Group Databasebeta| order | 24960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9437184 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C43 |
| abelian | C3×C42×C5×C8×C13 |
| multiplicative | (ℤ/28249)ˣ, (ℤ/32185)ˣ, (ℤ/33865)ˣ, (ℤ/34645)ˣ, (ℤ/56498)ˣ, (ℤ/64370)ˣ, (ℤ/67730)ˣ, (ℤ/69290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4 | C23×C3×C5×C13 |
| socle, prime radical | C23×C3×C5×C13 | C22×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1632 conjugacy classes of subgroups.
24960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.