Finite Group DatabasebetaFinite Group Databasebeta| order | 19872 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3649536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C42×C9×C23 |
| multiplicative | (ℤ/22607)ˣ, (ℤ/25715)ˣ, (ℤ/26315)ˣ, (ℤ/29015)ˣ, (ℤ/30747)ˣ, (ℤ/32331)ˣ, (ℤ/37305)ˣ, (ℤ/37395)ˣ, (ℤ/40996)ˣ, (ℤ/43108)ˣ, (ℤ/45214)ˣ, (ℤ/51430)ˣ, (ℤ/52630)ˣ, (ℤ/58030)ˣ, (ℤ/61494)ˣ, (ℤ/64662)ˣ, (ℤ/74610)ˣ, (ℤ/74790)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C32×C23 |
| socle, prime radical | C23×C32×C23 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
19872 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C37×C47 |
| outer automorphism group of | C13×C37×C47 |
Past the SmallGroups library coverage — no SmallGroups id.