Finite Group DatabasebetaFinite Group Databasebeta| order | 16660 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic85 |
| derived, Hall | C5×C17 ⋊ C4×C49 |
| Hall | C5×C17×C49 ⋊ C4 |
| Hall | C17×C49 ⋊ Dic5 |
| Hall | C5×C49 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic5×C49 |
| Sylow | C5 ⋊ C49×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D85 |
| commutator, hypocenter | C5×C17 | C4×C49 |
| Frattini | C2×C7 | C7×D85 |
| Fitting | C2×C5×C17×C49 | C2 |
| socle, prime radical, cosocle | C2×C5×C7×C17 | C2×C7 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C2×C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16660 |
4312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16660, 6);