Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#14523149 |
| Fitting, socle, Hall | C7×C132 ⋊ C3×C4 |
| derived, Sylow | C132 ⋊ C3×C4×C7 |
| Hall | C7×#10621730 ⋊ C3 |
| Hall | C7×#92789 ⋊ C4 |
| Hall | #10621730 ⋊ C3×C7 |
| Hall | #92789 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #14523149 |
| commutator, hypocenter | C132 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C132 | C3×C4 |
| prime radical | C7×#11759818 | C2 |
| cosocle | C13×D13 | C2×C3×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C7 | |
50 conjugacy classes of subgroups.
203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 191);