Finite Group DatabasebetaFinite Group Databasebeta| order | 13734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C109 ⋊ C2×C9 |
| Hall | #20293540 ⋊ C2 |
| Hall | D7×C109 ⋊ C9 |
| Sylow | C109 ⋊ D7⋊C9 |
| Hall | D7 ⋊ #11758281 |
| Sylow | C7 ⋊ C2×#11758281 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C109 | C2×C9 |
| prime radical | D7×C109⋊C3 | C3 |
| cosocle | C7×C109⋊C3 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 763 |
Polycyclic presentation:
2,3^2,7,109|b^3=c,d^a=d^6,d^b=d^2,e^b=e^16,e^c=e^6381 conjugacy classes — view the full character table.
| maximal subgroup of | #28351533⋊C2, C2×#28351535 |
| maximal normal subgroup of | #28351533⋊C2, C2×#28351535 |
| maximal quotient of | #42117400, C2×#28351535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13734, 29);