Finite Group DatabasebetaFinite Group Databasebeta| order | 17754 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C269 · Schur multiplier (H2) = C1 |
| direct product | D33×C269 |
| unambiguous semidirect product | C3⋊(D11×C269) |
| unambiguous semidirect product | C11⋊(D3×C269) |
| Fitting, socle, Hall | C3×C11×C269 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C269 |
| Hall | C11×C269 ⋊ D3 |
| Hall | C3×C269 ⋊ D11 |
| Sylow | C11 ⋊ D3×C269 |
| Sylow | C3 ⋊ D11×C269 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C269 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C269 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C269 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C269 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8877 |
4842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D269, D3×D11×C269, D33⋊D269, … |
| maximal normal subgroup of | D33×D269, D3×D11×C269, D33⋊D269, … |
| maximal quotient of | Dic33×C269, C2×D33×C269 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17754, 7);