Finite Group DatabasebetaFinite Group Databasebeta| order | 20640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7225344 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C5×C43 |
| multiplicative | (ℤ/39963)ˣ, (ℤ/42904)ˣ, (ℤ/44824)ˣ, (ℤ/45255)ˣ, (ℤ/48272)ˣ, (ℤ/51640)ˣ, (ℤ/53284)ˣ, (ℤ/60340)ˣ, (ℤ/61968)ˣ, (ℤ/62064)ˣ, (ℤ/64356)ˣ, (ℤ/67236)ˣ, (ℤ/68508)ˣ, (ℤ/77460)ˣ, (ℤ/77580)ˣ, (ℤ/79926)ˣ, (ℤ/90510)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C5×C43 |
| socle, prime radical | C24×C3×C5×C43 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
20640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.