Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#17990042 |
| derived, Hall | C3×C132⋊C7 ⋊ C4 |
| Hall | C132⋊C7 ⋊ Dic3 |
| Hall | C3×C132 ⋊ Dic7 |
| Sylow | C132 ⋊ Dic21 |
| Sylow | C3 ⋊ #17990042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#14556975 |
| commutator, hypocenter | C3×C132⋊C7 | C4 |
| Fitting, socle | C2×C3×C132 | D7 |
| prime radical, cosocle | C2×C3×C132⋊C7 | C2 |
| LCS | G ▷ C3×C132⋊C7 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13^2,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^2e,e^a=d^10e^11,d^c=d^6e^8,e^c=d^3e^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 83);