Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1 |
| direct product | C11×C19×#261 |
| Fitting, socle, Hall | C11×C13×C19 ⋊ C4 |
| derived, Sylow | C13 ⋊ C4×C11×C19 |
| Hall | C13×C19 ⋊ C4×C11 |
| Hall | C11×C13 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C19 | #261 |
| commutator, hypocenter | C13 | C4×C11×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C19 | C4 |
| prime radical | C11×C19×D13 | C2 |
| cosocle | D13 | C2×C11×C19 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C11×C19 | |
24 conjugacy classes of subgroups.
1463 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C19×AGL(1,𝔽13), C11×#15688302, C11×#15688303, … |
| maximal normal subgroup of | C11×C19×AGL(1,𝔽13), C11×#15688302, C11×#15688303, … |
| maximal quotient of | C3×C11×C19×#261, C11×C19×C3⋊#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 10);