Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#10621721 |
| Fitting, derived, Hall | C7×C169 ⋊ C3×C4 |
| Hall | C7⋊#10621721 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C169 ⋊ C4 |
| Sylow | C169 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ #10621721 |
| Sylow | C7 ⋊ C3×#10621721 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C169 | C3×C4 |
| Frattini | C13 | ΓL(1,𝔽8)⋊#261 |
| socle | C7×C13 | C3×#261 |
| prime radical | ΓL(1,𝔽8)×D169 | C2 |
| cosocle | C7×D169 | C2×C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7,13^2|a^2=c,e^13=f^2,d^a=d^6,e^a=e^8f,f^a=f^8,d^b=d^4,e^c=e^12f^11,f^c=f^12224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 31);