Finite Group DatabasebetaFinite Group Databasebeta| order | 17286 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2881 |
| Fitting, socle, Hall | C3×C43×C67 ⋊ C2 |
| derived, Hall | C43×C67 ⋊ C2×C3 |
| Hall | C3×C67 ⋊ D43 |
| Hall | C3×C43 ⋊ D67 |
| Sylow | C67 ⋊ C3×D43 |
| Sylow | C43 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2881 |
| commutator, cosocle, hypocenter | C43×C67 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C67 | C2 |
| LCS | G ▷ C43×C67 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8643 |
4326 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D43×D67, D3×D2881, D129⋊D67, … |
| maximal normal subgroup of | C3×D43×D67, D3×D2881, D129⋊D67, … |
| maximal quotient of | C3×Dic2881, C2×C3×D2881 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17286, 8);