Finite Group DatabasebetaFinite Group Databasebeta| order | 16116 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×Dic51 |
| unambiguous semidirect product | C3⋊(Dic17×C79) |
| derived, Hall | C3×C17 ⋊ C4×C79 |
| Hall | C3×C17×C79 ⋊ C4 |
| Hall | C17×C79 ⋊ Dic3 |
| Hall | C3×C79 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C79 |
| Sylow | C3 ⋊ Dic17×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | D51 |
| commutator, hypocenter | C3×C17 | C4×C79 |
| Frattini | C2 | C79×D51 |
| Fitting, socle, prime radical | C2×C3×C17×C79 | C2 |
| cosocle | C2×C3×C17 | C2×C79 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16116 |
4266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16116, 8);