Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×D37 |
| unambiguous semidirect product | (D5×C37)⋊(C2×C11) |
| unambiguous semidirect product | (C5×D37)⋊(C2×C11) |
| unambiguous semidirect product | D185⋊(C2×C11) |
| Fitting, socle, Hall | C5×C11×C37 ⋊ C22 |
| derived, Hall | C5×C37 ⋊ C22×C11 |
| Hall | C11×C37 ⋊ C2×D5 |
| Hall | C5×C11 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D5×C11 |
| Sylow | C5 ⋊ C2×C11×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×D37 |
| commutator, hypocenter | C5×C37 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C37 | C22 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
880 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C11×D37⋊C3, C3×D5×C11×D37, C11×D15×D37, … |
| maximal normal subgroup of | D5×C11×D37⋊C3, C3×D5×C11×D37 |
| maximal quotient of | C3×D5×C11×D37, C11×D15×D37, D5×C11×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 33);