Finite Group DatabasebetaFinite Group Databasebeta| order | 8066 |
| automorphism | Aut(G) order 15680304 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4033 |
| unambiguous semidirect product | C37⋊D109 |
| unambiguous semidirect product | C109⋊D37 |
| Fitting, socle, derived, Hall | C37×C109 ⋊ C2 |
| Sylow | C109 ⋊ D37 |
| Sylow | C37 ⋊ D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C109 | C2 |
| LCS | G ▷ C37×C109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,109|b^a=b^36,c^a=c^1082018 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30633210, #30633211, D37×D109, … |
| maximal normal subgroup of | #30633210, #30633211, D37×D109, … |
| maximal quotient of | Dic4033, C2×D4033, C3×D4033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8066, 3);