Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #20296858⋊C2 |
| unambiguous semidirect product | #20296862⋊C2 |
| unambiguous semidirect product | #20296864⋊C2 |
| Fitting, derived, Hall | C7×C169 ⋊ C22×C3 |
| Hall | D7×D169 ⋊ C3 |
| Hall | #16813063 ⋊ C22 |
| Sylow | C169 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C169 | C22×C3 |
| Frattini | C13 | #10587716⋊C2 |
| socle | C7×C13 | C2×D13⋊C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,13^2|e^13=f^12,e^a=e^12f,f^a=f^12,d^b=d^6,d^c=d^2,e^c=e^3f^2,f^c=f^3154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 37);