Finite Group DatabasebetaFinite Group Databasebeta| order | 3740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic187 |
| derived, Hall | C11×C17 ⋊ C4×C5 |
| Hall | C5×C11×C17 ⋊ C4 |
| Hall | C5×C17 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic17 |
| Sylow | C17 ⋊ C5×Dic11 |
| Sylow | C11 ⋊ C5×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D187 |
| commutator, hypocenter | C11×C17 | C4×C5 |
| Frattini | C2 | C5×D187 |
| Fitting, socle, prime radical | C2×C5×C11×C17 | C2 |
| cosocle | C2×C11×C17 | C2×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3740 |
950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic187, C5×Dic561, (C11⋊C25)⋊Dic17, … |
| maximal normal subgroup of | C3×C5×Dic187, (C11⋊C25)⋊Dic17, C25×Dic187, … |
| maximal quotient of | C3×C5×Dic187, C5×Dic561, C25×Dic187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3740, 8);