Finite Group DatabasebetaFinite Group Databasebeta| order | 15666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D373⋊C3 |
| unambiguous semidirect product | D373⋊(C3×C7) |
| unambiguous semidirect product | (C373⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C373 ⋊ C2×C3 |
| derived, Sylow | C373 ⋊ C2×C3×C7 |
| Hall | C7×C373⋊C3 ⋊ C2 |
| Hall | C7×D373 ⋊ C3 |
| Hall | C373⋊C3 ⋊ C2×C7 |
| Hall | D373 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D373⋊C3 |
| commutator, cosocle, hypocenter | C373 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C373 | C2×C3 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2611 |
476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#13093637⋊C3, #44531275, D7×D373⋊C3, … |
| maximal normal subgroup of | C7×#13093637⋊C3, #44531275, D7×D373⋊C3, … |
| maximal quotient of | C7×Dic373⋊C3, C2×C7×D373⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15666, 13);