Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1197 |
| unambiguous semidirect product | C7⋊(C7×D171) |
| unambiguous semidirect product | C9⋊(C7×D133) |
| unambiguous semidirect product | C19⋊(C7×D63) |
| Fitting, Hall | C72×C9×C19 ⋊ C2 |
| derived | C7×C9×C19 ⋊ C2×C7 |
| Hall | C72×C19 ⋊ D9 |
| Hall | C72×C9 ⋊ D19 |
| Hall | C9×C19 ⋊ C7×D7 |
| Sylow | C72 ⋊ D171 |
| Sylow | C19 ⋊ C7×D63 |
| Sylow | C9 ⋊ C7×D133 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1197 |
| commutator, cosocle, hypocenter | C7×C9×C19 | C2×C7 |
| Frattini | C3 | C7×D399 |
| Fitting | C72×C9×C19 | C2 |
| socle | C3×C72×C19 | D3 |
| LCS | G ▷ C7×C9×C19 | |
| UCS | C1 ◁ C7 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
4200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D63, C7×D7×D171, C7×D9×D133, … |
| maximal normal subgroup of | C7×D19×D63, C7×D7×D171, C7×D9×D133, … |
| maximal quotient of | C7×Dic1197, C2×C7×D1197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 158);