Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C7×C169 ⋊ C3×C4 |
| Hall | C7×#10621721 ⋊ C3 |
| Hall | #16813063 ⋊ C4 |
| Hall | #10621721 ⋊ ΓL(1,𝔽8) |
| Sylow | C169 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #10621721⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C169 | C3×C4 |
| Frattini | C13 | #11763982 |
| socle | C7×C13 | AGL(1,𝔽13) |
| prime radical | #20296858 | 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,e^a=e^8f,f^a=f^8,d^b=d^2,e^b=e^3f^9,f^b=f^3,e^c=e^12f^11,f^c=f^12118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 30);