Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 207360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C8×C11×C81 |
| multiplicative | (ℤ/43521)ˣ, (ℤ/57032)ˣ, (ℤ/57056)ˣ, (ℤ/58028)ˣ, (ℤ/85548)ˣ, (ℤ/86508)ˣ, (ℤ/87042)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C27 | C23×C3×C11 |
| socle, prime radical | C23×C3×C11 | C4×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
380 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.