Finite Group DatabasebetaFinite Group Databasebeta| order | 14740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C67⋊C11)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C67⋊AGL(1,𝔽5))⋊C11 |
| Fitting, socle, derived, Hall | C5×C67 ⋊ C4×C11 |
| Hall | C5×C67⋊C11 ⋊ C4 |
| Hall | C67⋊AGL(1,𝔽5) ⋊ C11 |
| Hall | C67⋊C11 ⋊ AGL(1,𝔽5) |
| Sylow | C67 ⋊ C11×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C67 | C4×C11 |
| prime radical | D5×C67⋊C11 | C2 |
| cosocle | D5×C67 | C2×C11 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 335 |
Polycyclic presentation:
2,11,2,5,67|a^2=c,d^a=d^2,e^a=e^66,e^b=e^64,d^c=d^467 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14740, 18);