Finite Group DatabasebetaFinite Group Databasebeta| order | 17028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic11×C43⋊C9 |
| unambiguous semidirect product | C11⋊(C4×C43⋊C9) |
| unambiguous semidirect product | (C43×Dic11)⋊C9 |
| derived, Hall | C11×C43 ⋊ C4×C9 |
| Hall | C11×C43⋊C9 ⋊ C4 |
| Hall | C43×Dic11 ⋊ C9 |
| Sylow | C43 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ C4×C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D11×C43⋊C3 |
| commutator, hypocenter | C11×C43 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C11×C43 | C2×C3 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17028 |
714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17028, 11);