Finite Group DatabasebetaFinite Group Databasebeta| order | 11774 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C841 · Schur multiplier (H2) = C1 |
| direct product | D7×C841 |
| unambiguous semidirect product | C7⋊(C2×C841) |
| Fitting, Hall | C7×C841 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C841 | D7 |
| commutator, hypocenter | C7 | C2×C841 |
| Frattini | C29 | D7×C29 |
| Fitting | C7×C841 | C2 |
| socle, cosocle | C7×C29 | C2×C29 |
| prime radical | D7×C29 | C29 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C841 | |
12 conjugacy classes of subgroups.
4205 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D841, C2×D7×C841, AGL(1,𝔽7)×C841, … |
| maximal normal subgroup of | D7×D841, C2×D7×C841, AGL(1,𝔽7)×C841, … |
| maximal quotient of | Dic7×C841, C2×D7×C841, C3×D7×C841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11774, 4);