Finite Group DatabasebetaFinite Group Databasebeta| order | 24640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 35389440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C5×C7×C11 |
| multiplicative | (ℤ/36685)ˣ, (ℤ/50025)ˣ, (ℤ/52635)ˣ, (ℤ/56144)ˣ, (ℤ/66700)ˣ, (ℤ/70180)ˣ, (ℤ/73370)ˣ, (ℤ/100050)ˣ, (ℤ/105270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C5×C7×C11 |
| socle, prime radical | C24×C5×C7×C11 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1992 conjugacy classes of subgroups.
24640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.