Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2332650700800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C33 |
| abelian | C25×C32×C9×C11 |
| multiplicative | (ℤ/71288)ˣ, (ℤ/91656)ˣ, (ℤ/100296)ˣ, (ℤ/101304)ˣ, (ℤ/106932)ˣ, (ℤ/110124)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C25×C33×C11 |
| socle, prime radical | C25×C33×C11 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
37400 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.