Finite Group DatabasebetaFinite Group Databasebeta| order | 13134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D597 |
| unambiguous semidirect product | C3⋊(C11×D199) |
| Fitting, socle, Hall | C3×C11×C199 ⋊ C2 |
| derived, Hall | C3×C199 ⋊ C2×C11 |
| Hall | C11×C199 ⋊ D3 |
| Sylow | C199 ⋊ D3×C11 |
| Hall | C3×C11 ⋊ D199 |
| Sylow | C3 ⋊ C11×D199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D597 |
| commutator, cosocle, hypocenter | C3×C199 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C199 | C2 |
| LCS | G ▷ C3×C199 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
3300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D199, D11×D597, D33⋊D199, … |
| maximal normal subgroup of | D3×C11×D199, D11×D597, D33⋊D199, … |
| maximal quotient of | C11×Dic597, C2×C11×D597, C11×D1791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13134, 9);