Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D11×D37 |
| Fitting, socle, Hall | C5×C11×C37 ⋊ C22 |
| derived, Hall | C11×C37 ⋊ C22×C5 |
| 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 | C5 | D11×D37 |
| commutator, hypocenter | C11×C37 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C37 | C22 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D11×D37⋊C3, C3×C5×D11×D37, C5×D33×D37, … |
| maximal normal subgroup of | C5×D11×D37⋊C3, C3×C5×D11×D37 |
| maximal quotient of | C3×C5×D11×D37, C5×D33×D37, C5×D11×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 23);