Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| isoclinism | isoclinic class of D161 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×D161 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D161 |
| commutator, cosocle, hypocenter | C7×C23 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C23 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C3×C11 | |
32 conjugacy classes of subgroups.
2706 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×D7×D23, C3×D11×D161, C3×D77⋊D23, … |
| maximal normal subgroup of | C3×C11×D7×D23, C3×D11×D161, C3×D77⋊D23, … |
| maximal quotient of | C3×C11×Dic161, C2×C3×C11×D161, C9×C11×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 9);