Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 566231040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5 |
| abelian | C22×C4×C52×C8×C9 |
| multiplicative | (ℤ/42845)ˣ, (ℤ/50061)ˣ, (ℤ/58425)ˣ, (ℤ/59368)ˣ, (ℤ/60225)ˣ, (ℤ/60885)ˣ, (ℤ/63712)ˣ, (ℤ/66748)ˣ, (ℤ/77900)ˣ, (ℤ/80300)ˣ, (ℤ/85690)ˣ, (ℤ/89052)ˣ, (ℤ/100122)ˣ, (ℤ/110700)ˣ, (ℤ/116850)ˣ, (ℤ/120450)ˣ, (ℤ/121770)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C24×C3×C52 |
| socle, prime radical | C24×C3×C52 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
9120 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.