Finite Group DatabasebetaFinite Group Databasebeta| order | 6006 |
| automorphism | Aut(G) order 4324320 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3003 |
| unambiguous semidirect product | C3⋊D1001 |
| unambiguous semidirect product | C7⋊D429 |
| unambiguous semidirect product | C11⋊D273 |
| unambiguous semidirect product | C13⋊D231 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C11×C13 | C2 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,13|b^a=b^2,c^a=c^6,d^a=d^10,e^a=e^121503 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D231, D11×D273, D21×D143, … |
| maximal normal subgroup of | D13×D231, D11×D273, D21×D143, … |
| maximal quotient of | Dic3003, C2×D3003, D9009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6006, 20);