Finite Group DatabasebetaFinite Group Databasebeta| order | 17122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1223 |
| unambiguous semidirect product | C1223⋊(C2×C7) |
| Fitting, socle, Hall | C7×C1223 ⋊ C2 |
| derived, Sylow | C1223 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1223 |
| commutator, cosocle, hypocenter | C1223 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C1223 | C2 |
| LCS | G ▷ C1223 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8561 |
4291 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D1223, C2×C7×D1223 |
| maximal normal subgroup of | D7×D1223, C2×C7×D1223 |
| maximal quotient of | C7×Dic1223, C2×C7×D1223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17122, 2);