Finite Group DatabasebetaFinite Group Databasebeta| order | 16638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2773 |
| unambiguous semidirect product | C47⋊(C3×D59) |
| unambiguous semidirect product | C59⋊(C3×D47) |
| Fitting, socle, Hall | C3×C47×C59 ⋊ C2 |
| derived, Hall | C47×C59 ⋊ C2×C3 |
| Hall | C3×C59 ⋊ D47 |
| Hall | C3×C47 ⋊ D59 |
| Sylow | C59 ⋊ C3×D47 |
| Sylow | C47 ⋊ C3×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2773 |
| commutator, cosocle, hypocenter | C47×C59 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C47×C59 | C2 |
| LCS | G ▷ C47×C59 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8319 |
4164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D47×D59, D3×D2773, D141⋊D59, … |
| maximal normal subgroup of | C3×D47×D59, D3×D2773, D141⋊D59, … |
| maximal quotient of | C3×Dic2773, C2×C3×D2773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16638, 4);