Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic209 |
| unambiguous semidirect product | C11⋊(C13×Dic19) |
| unambiguous semidirect product | C19⋊(C13×Dic11) |
| derived, Hall | C11×C19 ⋊ C4×C13 |
| Hall | C11×C13×C19 ⋊ C4 |
| Hall | C13×C19 ⋊ Dic11 |
| Hall | C11×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C13×Dic11 |
| Sylow | C11 ⋊ C13×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D209 |
| commutator, hypocenter | C11×C19 | C4×C13 |
| Frattini | C2 | C13×D209 |
| Fitting, socle, prime radical | C2×C11×C13×C19 | C2 |
| cosocle | C2×C11×C19 | C2×C13 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
2756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic209, C13×Dic627, C13×C11⋊((C19⋊C3)⋊C4), … |
| maximal normal subgroup of | C3×C13×Dic209, C13×C11⋊((C19⋊C3)⋊C4), C13⋊C3×Dic209, … |
| maximal quotient of | C3×C13×Dic209, C13×Dic627 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 6);