Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 73728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C5×C7×C32 |
| multiplicative | (ℤ/20467)ˣ, (ℤ/20863)ˣ, (ℤ/23527)ˣ, (ℤ/30249)ˣ, (ℤ/40934)ˣ, (ℤ/41726)ˣ, (ℤ/47054)ˣ, (ℤ/60498)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C22×C32×C5×C7 |
| socle, prime radical | C22×C32×C5×C7 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
408 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
| automorphism group of | C97×C211, C31×C673 |
| outer automorphism group of | C97×C211, C31×C673 |
Past the SmallGroups library coverage — no SmallGroups id.