Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×#92788⋊C7 |
| unambiguous semidirect product | (C22×#92788)⋊C7 |
| Fitting, socle, Hall | C22×C132 ⋊ C3×C7 |
| derived, Sylow | C132 ⋊ C22×C3×C7 |
| Hall | C22×C132⋊C7 ⋊ C3 |
| Hall | C22×#92788 ⋊ C7 |
| Hall | C132⋊C7 ⋊ C22×C3 |
| Hall | #92788 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92788⋊C7 |
| commutator, cosocle, hypocenter | C132 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C132 | C3×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 177);