Finite Group DatabasebetaFinite Group Databasebeta| order | 17886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D271⋊C3 |
| unambiguous semidirect product | D271⋊(C3×C11) |
| unambiguous semidirect product | (C271⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D271)⋊C3 |
| Fitting, socle, Hall | C11×C271 ⋊ C2×C3 |
| derived, Sylow | C271 ⋊ C2×C3×C11 |
| Hall | C11×C271⋊C3 ⋊ C2 |
| Hall | C11×D271 ⋊ C3 |
| Hall | C271⋊C3 ⋊ C2×C11 |
| Hall | D271 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D271⋊C3 |
| commutator, cosocle, hypocenter | C271 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C271 | C2×C3 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2981 |
561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D271⋊C3, C2×C11×D271⋊C3 |
| maximal normal subgroup of | D11×D271⋊C3, C2×C11×D271⋊C3 |
| maximal quotient of | C11×(C271⋊C3)⋊C4, C2×C11×D271⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17886, 10);