Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 126835752960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C43×C5 |
| abelian | C2×C32×C43×C52 |
| multiplicative | (ℤ/43615)ˣ, (ℤ/59475)ˣ, (ℤ/79300)ˣ, (ℤ/87230)ˣ, (ℤ/118950)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C24×C32×C52 |
| socle, prime radical | C24×C32×C52 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30528 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.