Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| isoclinism | isoclinic class of C169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×C169⋊C3 |
| unambiguous semidirect product | C169⋊(C32×C7) |
| unambiguous semidirect product | (C3×C169)⋊(C3×C7) |
| Fitting | C3×C7×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C32×C7 |
| Hall | C7×C169 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C32×C7 |
| Frattini | C13 | C3×C7×C13⋊C3 |
| Fitting | C3×C7×C169 | C3 |
| socle | C3×C7×C13 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C3×C7 | |
36 conjugacy classes of subgroups.
1239 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D169⋊C3, C3×D7×C169⋊C3, C3×(C169⋊C3)⋊D7, … |
| maximal normal subgroup of | C3×C7×D169⋊C3, C3×D7×C169⋊C3, C3×(C169⋊C3)⋊D7, … |
| maximal quotient of | C2×C3×C7×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 8);