Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C11×D37 |
| unambiguous semidirect product | C37⋊(C22×C5×C11) |
| unambiguous semidirect product | (C2×C37)⋊(C2×C5×C11) |
| Fitting, socle | C2×C5×C11×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C22×C5×C11 |
| Hall | C5×C11×C37 ⋊ C22 |
| Hall | C11×C37 ⋊ C22×C5 |
| Hall | C5×C37 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | D37 |
| commutator, hypocenter | C37 | C22×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C5×C11 | |
40 conjugacy classes of subgroups.
2200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C11×D37⋊C3, C5×D3×C11×D37, C2×C3×C5×C11×D37, … |
| maximal normal subgroup of | C2×C5×C11×D37⋊C3, C2×C3×C5×C11×D37 |
| maximal quotient of | C5×D3×C11×D37, C2×C3×C5×C11×D37, C2×C5×C11×D111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 46);