Finite Group DatabasebetaFinite Group Databasebeta| order | 13734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×#11758281 |
| Fitting, socle, Hall | C2×C7×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C2×C7×C9 |
| Hall | C7×C109 ⋊ C2×C9 |
| Hall | C2×C109 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #11758281 |
| commutator, hypocenter | C109 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C109 | C9 |
| prime radical | C2×C7×C109⋊C3 | C3 |
| cosocle | C109⋊C3 | C2×C3×C7 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1526 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#16840993, #42117407, Dic7×#11758281, … |
| maximal normal subgroup of | C7×#16840993, #42117407, Dic7×#11758281, … |
| maximal quotient of | C4×C7×#11758281, C22×C7×#11758281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13734, 38);