Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#14556975⋊C2 |
| Fitting, socle, Hall | C3×C132 ⋊ C2×D7 |
| derived, Hall | C132⋊C7 ⋊ C22×C3 |
| Hall | C3×C132⋊C7 ⋊ C22 |
| Sylow | C132 ⋊ C2×C3×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14556975⋊C2 |
| commutator, cosocle, hypocenter | C132⋊C7 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132 | C2×D7 |
| LCS | G ▷ C132⋊C7 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 168);