Finite Group DatabasebetaFinite Group Databasebeta| order | 22464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 111476736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43 |
| abelian | C3×C43×C9×C13 |
| multiplicative | (ℤ/25493)ˣ, (ℤ/29045)ˣ, (ℤ/31265)ˣ, (ℤ/50986)ˣ, (ℤ/58090)ˣ, (ℤ/62530)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C3 | C23×C32×C13 |
| socle, prime radical | C23×C32×C13 | C23×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2580 conjugacy classes of subgroups.
22464 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.