Finite Group DatabasebetaFinite Group Databasebeta| order | 12014 |
| automorphism | Aut(G) order 36078042 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6007 |
| unambiguous semidirect product | C6007⋊C2 |
| Fitting, socle, derived, Sylow | C6007 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6007 | C2 |
| LCS | G ▷ C6007 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6007|b^a=b^60063005 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6007, D6007⋊C3, C3×D6007, … |
| maximal normal subgroup of | C2×D6007, D6007⋊C3, C3×D6007 |
| maximal quotient of | Dic6007, C2×D6007, C3×D6007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12014, 1);