Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| isoclinism | isoclinic class of D203 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D203 |
| unambiguous semidirect product | C7⋊(C29×D29) |
| unambiguous semidirect product | C29⋊(D7×C29) |
| Fitting, socle, Hall | C7×C292 ⋊ C2 |
| derived | C7×C29 ⋊ C2×C29 |
| Sylow | C292 ⋊ D7 |
| Sylow | C7 ⋊ C29×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D203 |
| commutator, cosocle, hypocenter | C7×C29 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C2 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C29 | |
44 conjugacy classes of subgroups.
2987 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C29×D29, D29×D203, D203⋊D29, … |
| maximal normal subgroup of | D7×C29×D29, D29×D203, D203⋊D29, … |
| maximal quotient of | C29×Dic203, C2×C29×D203, C3×C29×D203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 30);