Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | Aut(G) order 5860800 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4070 |
| direct product | C2×D2035 |
| unambiguous semidirect product | (C2×C5)⋊D407 |
| unambiguous semidirect product | (C2×C11)⋊D185 |
| unambiguous semidirect product | (C2×C37)⋊D55 |
| Fitting, socle | C2×C5×C11×C37 ⋊ C2 |
| derived, Hall | C5×C11×C37 ⋊ C22 |
| Hall | C11×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D55 |
| Sylow | C11 ⋊ C2×D185 |
| Sylow | C5 ⋊ C2×D407 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2035 |
| commutator, hypocenter | C5×C11×C37 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C37 | C2 |
| LCS | G ▷ C5×C11×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(C11⋊(D37⋊C3)), D3×D2035, C2×C3×D2035, … |
| maximal normal subgroup of | C2×C5⋊(C11⋊(D37⋊C3)), C2×C3×D2035, D8140 |
| maximal quotient of | D3×D2035, C2×C3×D2035, C2×D6105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 40);