Finite Group DatabasebetaFinite Group Databasebeta| order | 17706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D681 |
| unambiguous semidirect product | C3⋊(C13×D227) |
| unambiguous semidirect product | C227⋊(D3×C13) |
| Fitting, socle, Hall | C3×C13×C227 ⋊ C2 |
| derived, Hall | C3×C227 ⋊ C2×C13 |
| Hall | C13×C227 ⋊ D3 |
| Sylow | C227 ⋊ D3×C13 |
| Hall | C3×C13 ⋊ D227 |
| Sylow | C3 ⋊ C13×D227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D681 |
| commutator, cosocle, hypocenter | C3×C227 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C227 | C2 |
| LCS | G ▷ C3×C227 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8853 |
4446 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D227, D13×D681, D39⋊D227, … |
| maximal normal subgroup of | D3×C13×D227, D13×D681, D39⋊D227, … |
| maximal quotient of | C13×Dic681, C2×C13×D681 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17706, 7);