Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 63700992 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43 |
| abelian | C3×C42×C16×C27 |
| multiplicative | (ℤ/24089)ˣ, (ℤ/28145)ˣ, (ℤ/48178)ˣ, (ℤ/56290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8×C9 | C23×C32 |
| socle, prime radical | C23×C32 | C22×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3906 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C17×C109 |
| outer automorphism group of | C13×C17×C109 |
Past the SmallGroups library coverage — no SmallGroups id.