Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 21233664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C5×C7×C9 |
| multiplicative | (ℤ/30305)ˣ, (ℤ/35409)ˣ, (ℤ/39405)ˣ, (ℤ/41325)ˣ, (ℤ/41992)ˣ, (ℤ/42032)ˣ, (ℤ/43065)ˣ, (ℤ/47212)ˣ, (ℤ/50480)ˣ, (ℤ/50800)ˣ, (ℤ/52540)ˣ, (ℤ/55100)ˣ, (ℤ/60610)ˣ, (ℤ/62988)ˣ, (ℤ/70818)ˣ, (ℤ/78300)ˣ, (ℤ/78810)ˣ, (ℤ/82650)ˣ, (ℤ/86130)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C24×C3×C5×C7 |
| socle, prime radical | C24×C3×C5×C7 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2988 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.