Finite Group DatabasebetaFinite Group Databasebeta| order | 7022 |
| automorphism | Aut(G) order 12323610 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3511 |
| unambiguous semidirect product | C3511⋊C2 |
| Fitting, socle, derived, Sylow | C3511 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3511 | C2 |
| LCS | G ▷ C3511 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3511|b^a=b^35101757 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3511, D3511⋊C3, C3×D3511, … |
| maximal normal subgroup of | C2×D3511, D3511⋊C3, C3×D3511, … |
| maximal quotient of | Dic3511, C2×D3511, C3×D3511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7022, 1);