Finite Group DatabasebetaFinite Group Databasebeta| order | 7018 |
| automorphism | Aut(G) order 10807720 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3509 |
| unambiguous semidirect product | C29⋊D121 |
| unambiguous semidirect product | C121⋊D29 |
| Fitting, derived, Hall | C29×C121 ⋊ C2 |
| Sylow | C121 ⋊ D29 |
| Sylow | C29 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C29×C121 | C2 |
| Frattini | C11 | D319 |
| socle | C11×C29 | D11 |
| LCS | G ▷ C29×C121 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,29,11|b^11=d^10,b^a=b^10d,c^a=c^28,d^a=d^101756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D121, C2×D3509, C3×D3509, … |
| maximal normal subgroup of | D29×D121, C2×D3509, C3×D3509, … |
| maximal quotient of | Dic3509, C2×D3509, C3×D3509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7018, 4);