Finite Group DatabasebetaFinite Group Databasebeta| order | 22464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 19874709504 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C33×C4 |
| abelian | C22×C33×C42×C13 |
| multiplicative | (ℤ/35945)ˣ, (ℤ/42861)ˣ, (ℤ/43407)ˣ, (ℤ/46215)ˣ, (ℤ/49455)ˣ, (ℤ/53235)ˣ, (ℤ/57148)ˣ, (ℤ/71890)ˣ, (ℤ/73476)ˣ, (ℤ/85722)ˣ, (ℤ/86814)ˣ, (ℤ/92430)ˣ, (ℤ/98910)ˣ, (ℤ/106470)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C33×C13 |
| socle, prime radical | C24×C33×C13 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
13944 conjugacy classes of subgroups.
22464 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.