Finite Group DatabasebetaFinite Group Databasebeta| order | 16660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic833 |
| unambiguous semidirect product | C49⋊(C5×Dic17) |
| derived, Hall | C17×C49 ⋊ C4×C5 |
| Hall | C5×C17×C49 ⋊ C4 |
| Hall | C5×C49 ⋊ Dic17 |
| Hall | C5×C17 ⋊ Dic49 |
| Sylow | C49 ⋊ C5×Dic17 |
| Sylow | C17 ⋊ C5×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D833 |
| commutator, hypocenter | C17×C49 | C4×C5 |
| Frattini | C2×C7 | C5×D119 |
| Fitting | C2×C5×C17×C49 | C2 |
| socle, prime radical | C2×C5×C7×C17 | D7 |
| cosocle | C2×C17×C49 | C2×C5 |
| LCS | G ▷ C17×C49 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16660 |
4180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16660, 4);