Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D143 |
| unambiguous semidirect product | (C11×D19)⋊D13 |
| unambiguous semidirect product | (C13×D19)⋊D11 |
| Fitting, socle, derived, Hall | C11×C13×C19 ⋊ C22 |
| Hall | C13×C19 ⋊ C2×D11 |
| Hall | C11×C19 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D143 |
| Sylow | C13 ⋊ D11×D19 |
| Sylow | C11 ⋊ D13×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C19 | C22 |
| LCS | G ▷ C11×C13×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
803 conjugacy classes — view the full character table.
| maximal subgroup of | #13093360⋊D11, #13093361⋊D11, D19×C11⋊(D13⋊C3), … |
| maximal normal subgroup of | #13093360⋊D11, #13093361⋊D11, D19×C11⋊(D13⋊C3), … |
| maximal quotient of | C3×D19×D143, D19×D429, D57×D143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 16);