Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C11⋊#3866 |
| Fitting, socle, Hall | C5×C11×C37 ⋊ C4 |
| derived, Hall | C11×C37 ⋊ C4×C5 |
| Hall | C5×C37 ⋊ Dic11 |
| Hall | C5×C11 ⋊ #3866 |
| Sylow | C37 ⋊ C5×Dic11 |
| Sylow | C11 ⋊ C5×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊#3866 |
| commutator, hypocenter | C11×C37 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C37 | C4 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
565 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C11⋊(#3866⋊C3), C3×C5×C11⋊#3866, C5×C3⋊(C11⋊#3866) |
| maximal normal subgroup of | C5×C11⋊(#3866⋊C3), C3×C5×C11⋊#3866 |
| maximal quotient of | C3×C5×C11⋊#3866, C5×C3⋊(C11⋊#3866) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 22);