Finite Group DatabasebetaFinite Group Databasebeta| order | 17066 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1219 |
| unambiguous semidirect product | C23⋊(C7×D53) |
| unambiguous semidirect product | C53⋊(C7×D23) |
| Fitting, socle, Hall | C7×C23×C53 ⋊ C2 |
| derived, Hall | C23×C53 ⋊ C2×C7 |
| Hall | C7×C53 ⋊ D23 |
| Hall | C7×C23 ⋊ D53 |
| Sylow | C53 ⋊ C7×D23 |
| Sylow | C23 ⋊ C7×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1219 |
| commutator, cosocle, hypocenter | C23×C53 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C53 | C2 |
| LCS | G ▷ C23×C53 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8533 |
4277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D23×D53, D7×D1219, D161⋊D53, … |
| maximal normal subgroup of | C7×D23×D53, D7×D1219, D161⋊D53, … |
| maximal quotient of | C7×Dic1219, C2×C7×D1219 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17066, 4);