Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6193152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C5×C7×C8×C9 |
| multiplicative | (ℤ/41464)ˣ, (ℤ/41656)ˣ, (ℤ/42712)ˣ, (ℤ/43168)ˣ, (ℤ/44704)ˣ, (ℤ/60504)ˣ, (ℤ/60576)ˣ, (ℤ/60696)ˣ, (ℤ/61344)ˣ, (ℤ/62196)ˣ, (ℤ/62484)ˣ, (ℤ/64068)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C3×C5×C7 |
| socle, prime radical | C24×C3×C5×C7 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2028 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.