Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic247 |
| unambiguous semidirect product | C19⋊(C11×Dic13) |
| derived, Hall | C13×C19 ⋊ C4×C11 |
| Hall | C11×C13×C19 ⋊ C4 |
| Hall | C11×C19 ⋊ Dic13 |
| Hall | C11×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C11×Dic13 |
| Sylow | C13 ⋊ C11×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D247 |
| commutator, hypocenter | C13×C19 | C4×C11 |
| Frattini | C2 | C11×D247 |
| Fitting, socle, prime radical | C2×C11×C13×C19 | C2 |
| cosocle | C2×C13×C19 | C2×C11 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic247, C11×Dic741, C11×(C19⋊C3)⋊Dic13, … |
| maximal normal subgroup of | C3×C11×Dic247, C11×(C19⋊C3)⋊Dic13, C11×#15688282, … |
| maximal quotient of | C3×C11×Dic247, C11×Dic741 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 4);