Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| isoclinism | isoclinic class of D29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D29⋊C7 |
| unambiguous semidirect product | D29⋊(C7×C29) |
| unambiguous semidirect product | (C29⋊C7)⋊(C2×C29) |
| Fitting, socle, Sylow | C292 ⋊ C2×C7 |
| derived | C29 ⋊ C2×C7×C29 |
| Hall | C29×C29⋊C7 ⋊ C2 |
| Hall | C29×D29 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C292 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C29 | |
18 conjugacy classes of subgroups.
464 conjugacy classes — view the full character table.
| maximal subgroup of | C29×AGL(1,𝔽29), #37555409, D29×D29⋊C7, … |
| maximal normal subgroup of | C29×AGL(1,𝔽29), #37555409, D29×D29⋊C7, … |
| maximal quotient of | C29×Dic29⋊C7, C2×C29×D29⋊C7, C3×C29×D29⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 9);