Finite Group DatabasebetaFinite Group Databasebeta| order | 7018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊D319 |
| unambiguous semidirect product | C29⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C29 ⋊ C2 |
| Sylow | C112 ⋊ D29 |
| Sylow | C29 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C29 | C2 |
| LCS | G ▷ C112×C29 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,11^2,29|b^a=b^10,c^a=c^10,d^a=d^281756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×C11⋊D11, D11×D319, #28380559, … |
| maximal normal subgroup of | D29×C11⋊D11, D11×D319, #28380559, … |
| maximal quotient of | C11⋊Dic319, C2×C11⋊D319, C3×C11⋊D319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7018, 10);