Finite Group DatabasebetaFinite Group Databasebeta| order | 10686 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C137 · Schur multiplier (H2) = C1 |
| direct product | C3×D13×C137 |
| Fitting, socle, Hall | C3×C13×C137 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C3×C137 |
| Hall | C13×C137 ⋊ C2×C3 |
| Hall | C3×C13 ⋊ C2×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C137 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C137 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C137 | |
16 conjugacy classes of subgroups.
3288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#261×C137, C3×#20297119, C3×D13×D137, … |
| maximal normal subgroup of | C3×#261×C137, C3×#20297119, C3×D13×D137, … |
| maximal quotient of | C3×Dic13×C137, C2×C3×D13×C137, C9×D13×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10686, 4);