Finite Group DatabasebetaFinite Group Databasebeta| order | 28728 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 93312 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C7×C9×C19 |
| multiplicative | (ℤ/29083)ˣ, (ℤ/30343)ˣ, (ℤ/33523)ˣ, (ℤ/43101)ˣ, (ℤ/43119)ˣ, (ℤ/58166)ˣ, (ℤ/60686)ˣ, (ℤ/67046)ˣ, (ℤ/86202)ˣ, (ℤ/86238)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C7×C19 |
| socle, prime radical | C22×C32×C7×C19 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
28728 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.