Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C4×#92788⋊C7 |
| unambiguous semidirect product | (C4×#92788)⋊C7 |
| unambiguous semidirect product | (C4×C132⋊C7)⋊C3 |
| Fitting, Hall | C4×C132 ⋊ C3×C7 |
| derived, Sylow | C132 ⋊ C3×C4×C7 |
| Hall | C4×C132⋊C7 ⋊ C3 |
| Hall | C4×#92788 ⋊ C7 |
| Hall | C132⋊C7 ⋊ C3×C4 |
| Hall | #92788 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92788⋊C7 |
| commutator, hypocenter | C132 | C3×C4×C7 |
| Frattini | C2 | C2×#92788⋊C7 |
| Fitting | C4×C132 | C3×C7 |
| socle, cosocle | C2×C132 | C2×C3×C7 |
| prime radical | C2×#92788⋊C7 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C4 | |
36 conjugacy classes of subgroups.
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 80);