Finite Group DatabasebetaFinite Group Databasebeta| order | 3740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊Dic17 |
| unambiguous semidirect product | Dic187⋊C5 |
| derived, Hall | C11×C17 ⋊ C4×C5 |
| Hall | C17×C11⋊C5 ⋊ C4 |
| Hall | Dic187 ⋊ C5 |
| Hall | C11⋊C5 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ C5×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊AGL(1,𝔽11) |
| commutator, hypocenter | C11×C17 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C17 | C2×C5 |
| prime radical | C2×C17×C11⋊C5 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 748 |
Polycyclic presentation:
2,5,11,17,2|a^2=e,c^a=c^10,d^a=d^16,c^b=c^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3740, 4);