Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×C22⋊#63270 |
| unambiguous semidirect product | C22⋊(C13×#63270) |
| Fitting, socle, Hall | C22×C7×C132 ⋊ C3 |
| derived | C22×C7×C13 ⋊ C3×C13 |
| Hall | C7×C132 ⋊ A4 |
| Hall | C22×C132 ⋊ ΓL(1,𝔽8) |
| Sylow | C132 ⋊ C22⋊ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C13×C13⋊C3 |
| Sylow | C7 ⋊ C13×C22⋊(C13⋊C3) |
| Sylow | C22 ⋊ C13×#63270 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C22⋊#63270 |
| commutator, cosocle, hypocenter | C22×C7×C13 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C132 | C3 |
| LCS | G ▷ C22×C7×C13 | |
| UCS | C1 ◁ C13 | |
80 conjugacy classes of subgroups.
1612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 428);