Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#16813064 |
| Fitting, derived, Hall | C22×C7×C169 ⋊ C3 |
| Hall | C7×C169 ⋊ A4 |
| Hall | C22×C169 ⋊ ΓL(1,𝔽8) |
| Sylow | C169 ⋊ C22⋊ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C169⋊C3 |
| Sylow | C7 ⋊ C22⋊(C169⋊C3) |
| Sylow | C22 ⋊ #16813064 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C7×C169 | C3 |
| Frattini | C13 | C22⋊#63271 |
| socle | C22×C7×C13 | C13⋊C3 |
| LCS | G ▷ C22×C7×C169 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,7,13^2|e^13=f^6,b^a=c,c^a=bc,d^a=d^4,e^a=e^3f,f^a=f^31580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 68);