Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C3⋊#17990053 |
| Fitting, socle, Hall | C3×C132 ⋊ Dic7 |
| derived, Hall | C3×C132⋊C7 ⋊ C4 |
| Hall | C132⋊C7 ⋊ Dic3 |
| Sylow | C132 ⋊ Dic21 |
| Sylow | C3 ⋊ #17990053 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C132⋊C7 | C4 |
| Fitting, socle | C3×C132 | Dic7 |
| prime radical, cosocle | C3×(C13⋊D13)⋊C7 | C2 |
| LCS | G ▷ C3×C132⋊C7 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,13^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^7f^9,f^a=e^6f^6,e^b=e^12,f^b=f^12,e^d=e^9f^5,f^d=e^4f^1142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 175);