Finite Group DatabasebetaFinite Group Databasebeta| order | 22032 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 71663616 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C32×C4×C9×C17 |
| multiplicative | (ℤ/25441)ˣ, (ℤ/26677)ˣ, (ℤ/27937)ˣ, (ℤ/34299)ˣ, (ℤ/35919)ˣ, (ℤ/36153)ˣ, (ℤ/38619)ˣ, (ℤ/50882)ˣ, (ℤ/53354)ˣ, (ℤ/55874)ˣ, (ℤ/68598)ˣ, (ℤ/71838)ˣ, (ℤ/72306)ˣ, (ℤ/77238)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C33×C17 |
| socle, prime radical | C23×C33×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2700 conjugacy classes of subgroups.
22032 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.