Finite Group DatabasebetaFinite Group Databasebeta| order | 13734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D2289 |
| unambiguous semidirect product | C7⋊(C3⋊D327) |
| unambiguous semidirect product | C109⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C109 ⋊ C2 |
| Hall | C32×C109 ⋊ D7 |
| Hall | C7×C109 ⋊ C3⋊D3 |
| Sylow | C109 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D109 |
| Sylow | C32 ⋊ D763 |
| Sylow | C7 ⋊ C3⋊D327 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C109 | C2 |
| LCS | G ▷ C32×C7×C109 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6867 |
Polycyclic presentation:
2,3^2,7,109|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^1083435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2289, D21×D327, C3⋊D21×D109, … |
| maximal normal subgroup of | D3×D2289, D21×D327, C3⋊D21×D109, … |
| maximal quotient of | C3⋊Dic2289, C2×C3⋊D2289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13734, 74);