Finite Group DatabasebetaFinite Group Databasebeta| order | 7018 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | D29×C121 |
| unambiguous semidirect product | C29⋊(C2×C121) |
| Fitting, Hall | C29×C121 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D29 |
| commutator, hypocenter | C29 | C2×C121 |
| Frattini | C11 | C11×D29 |
| Fitting | C29×C121 | C2 |
| socle | C11×C29 | C2×C11 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1181×C121, C121⋊#1181, D29×D121, … |
| maximal normal subgroup of | #1181×C121, C121⋊#1181, D29×D121, … |
| maximal quotient of | Dic29×C121, C2×D29×C121, C3×D29×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7018, 3);