Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×D69 |
| unambiguous semidirect product | C3⋊(C7×C11×D23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C7×C11 | |
32 conjugacy classes of subgroups.
2772 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C11×D23, C7×D11×D69, C7×D33⋊D23, … |
| maximal normal subgroup of | D3×C7×C11×D23, C7×D11×D69, C7×D33⋊D23, … |
| maximal quotient of | C7×C11×Dic69, C2×C7×C11×D69, C7×C11×D207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 13);