Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C3⋊((C13⋊D13)⋊C7) |
| unambiguous semidirect product | (C2×C3)⋊((C13⋊D13)⋊C7) |
| unambiguous semidirect product | (C2×C3⋊(C13⋊D13))⋊C7 |
| Fitting, socle | C2×C3×C132 ⋊ C2×C7 |
| derived, Hall | C3×C132 ⋊ C22×C7 |
| Hall | C3×C132⋊C7 ⋊ C22 |
| Hall | C2×C3⋊(C13⋊D13) ⋊ C7 |
| Hall | C132⋊C7 ⋊ C2×D3 |
| Sylow | C132 ⋊ C2×D3×C7 |
| Sylow | C3 ⋊ C2×(C13⋊D13)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊((C13⋊D13)⋊C7) |
| commutator, cosocle, hypocenter | C3×C132 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C132 | C2×C7 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 183);