Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 127401984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C3×C4×C16×C27 |
| multiplicative | (ℤ/38913)ˣ, (ℤ/45032)ˣ, (ℤ/45465)ˣ, (ℤ/48195)ˣ, (ℤ/48496)ˣ, (ℤ/48832)ˣ, (ℤ/51884)ˣ, (ℤ/60620)ˣ, (ℤ/62352)ˣ, (ℤ/62784)ˣ, (ℤ/66708)ˣ, (ℤ/67392)ˣ, (ℤ/67548)ˣ, (ℤ/71604)ˣ, (ℤ/77826)ˣ, (ℤ/77940)ˣ, (ℤ/90930)ˣ, (ℤ/96390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C9 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7154 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.