Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11612160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C11×C81 |
| multiplicative | (ℤ/56235)ˣ, (ℤ/59984)ˣ, (ℤ/71320)ˣ, (ℤ/74980)ˣ, (ℤ/85584)ˣ, (ℤ/89424)ˣ, (ℤ/106980)ˣ, (ℤ/111780)ˣ, (ℤ/112470)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C27 | C24×C3×C11 |
| socle, prime radical | C24×C3×C11 | C2×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1180 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.