Finite Group DatabasebetaFinite Group Databasebeta| order | 17457 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C529⋊C11 |
| unambiguous semidirect product | C529⋊(C3×C11) |
| unambiguous semidirect product | (C3×C529)⋊C11 |
| Fitting, Hall | C3×C529 ⋊ C11 |
| derived, Sylow | C529 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C529⋊C11 |
| commutator, cosocle, hypocenter | C529 | C3×C11 |
| Frattini | C23 | C3×C23⋊C11 |
| Fitting | C3×C529 | C11 |
| socle | C3×C23 | C23⋊C11 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1587 |
177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D529⋊C11, D3×C529⋊C11, C3⋊(D529⋊C11), … |
| maximal normal subgroup of | C3×D529⋊C11, D3×C529⋊C11, C3⋊(D529⋊C11), … |
| maximal quotient of | C2×C3×C529⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17457, 2);