Finite Group DatabasebetaFinite Group Databasebeta| order | 8066 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D109 |
| unambiguous semidirect product | C109⋊(C2×C37) |
| Fitting, socle, Hall | C37×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D109 |
| commutator, hypocenter | C109 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
2072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#89137, #30633213, D37×D109, … |
| maximal normal subgroup of | C37×#89137, #30633213, D37×D109, … |
| maximal quotient of | C37×Dic109, C2×C37×D109, C3×C37×D109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8066, 2);