Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D407 |
| unambiguous semidirect product | (C2×C37)⋊(C5×D11) |
| Fitting, socle | C2×C5×C11×C37 ⋊ C2 |
| derived, Hall | C11×C37 ⋊ C22×C5 |
| Hall | C5×C11×C37 ⋊ C22 |
| Hall | C5×C37 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C5×D11 |
| Sylow | C11 ⋊ C2×C5×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D407 |
| commutator, hypocenter | C11×C37 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C37 | C2 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C11⋊(D37⋊C3), C5×D3×D407, C2×C3×C5×D407, … |
| maximal normal subgroup of | C2×C5×C11⋊(D37⋊C3), C2×C3×C5×D407 |
| maximal quotient of | C5×D3×D407, C2×C3×C5×D407, C2×C5×D1221 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 44);