Finite Group DatabasebetaFinite Group Databasebeta| order | 28386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C2×C83) |
| derived, Sylow | C19 ⋊ C2×C9×C83 |
| Hall | C83×#4294 ⋊ C2 |
| Hall | D19×C83 ⋊ C9 |
| Hall | C19×C83 ⋊ C2×C9 |
| Hall | #4294 ⋊ C2×C83 |
| Hall | D19 ⋊ C9×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C83 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C9×C83 |
| Frattini | C3 | C83×D19⋊C3 |
| Fitting, socle | C3×C19×C83 | C2×C3 |
| prime radical | C3×D19×C83 | C3 |
| cosocle | C3×C19 | C2×C3×C83 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C83 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14193 |
2241 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28386, 11);