Finite Group DatabasebetaFinite Group Databasebeta| order | 11594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D527 |
| unambiguous semidirect product | C17⋊(C11×D31) |
| unambiguous semidirect product | C31⋊(C11×D17) |
| Fitting, socle, Hall | C11×C17×C31 ⋊ C2 |
| derived, Hall | C17×C31 ⋊ C2×C11 |
| Hall | C11×C31 ⋊ D17 |
| Hall | C11×C17 ⋊ D31 |
| Sylow | C31 ⋊ C11×D17 |
| Sylow | C17 ⋊ C11×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D527 |
| commutator, cosocle, hypocenter | C17×C31 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C31 | C2 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
2915 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D17×D31, D11×D527, D187⋊D31, … |
| maximal normal subgroup of | C11×D17×D31, D11×D527, D187⋊D31, … |
| maximal quotient of | C11×Dic527, C2×C11×D527, C3×C11×D527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11594, 4);