Finite Group DatabasebetaFinite Group Databasebeta| order | 16766 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×D83 |
| unambiguous semidirect product | C83⋊(C2×C101) |
| Fitting, socle, Hall | C83×C101 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D83 |
| commutator, cosocle, hypocenter | C83 | C2×C101 |
| Frattini | C1 | G |
| Fitting, socle | C83×C101 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C101 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8383 |
4343 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D83×D101, C2×C101×D83 |
| maximal normal subgroup of | D83×D101, C2×C101×D83 |
| maximal quotient of | C101×Dic83, C2×C101×D83 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16766, 1);