Finite Group DatabasebetaFinite Group Databasebeta| order | 6666 |
| automorphism | Aut(G) order 6666000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3333 |
| unambiguous semidirect product | C3⋊D1111 |
| unambiguous semidirect product | C11⋊D303 |
| unambiguous semidirect product | C101⋊D33 |
| Fitting, socle, derived, Hall | C3×C11×C101 ⋊ C2 |
| Hall | C11×C101 ⋊ D3 |
| Hall | C3×C101 ⋊ D11 |
| Sylow | C101 ⋊ D33 |
| Hall | C3×C11 ⋊ D101 |
| Sylow | C11 ⋊ D303 |
| Sylow | C3 ⋊ D1111 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C101 | C2 |
| LCS | G ▷ C3×C11×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,101|b^a=b^2,c^a=c^10,d^a=d^1001668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D101, D11×D303, D3×D1111, … |
| maximal normal subgroup of | D33×D101, D11×D303, D3×D1111, … |
| maximal quotient of | Dic3333, C2×D3333, D9999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6666, 8);