Finite Group DatabasebetaFinite Group Databasebeta| order | 12022 |
| automorphism | Aut(G) order 36126110 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6011 |
| unambiguous semidirect product | C6011⋊C2 |
| Fitting, socle, derived, Sylow | C6011 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6011 | C2 |
| LCS | G ▷ C6011 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6011|b^a=b^60103007 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6011, C3×D6011, D18033 |
| maximal normal subgroup of | C2×D6011, C3×D6011 |
| maximal quotient of | Dic6011, C2×D6011, C3×D6011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12022, 1);