Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×Dic11 |
| derived, Sylow | C11 ⋊ C4×C5×C37 |
| Hall | C5×C11×C37 ⋊ C4 |
| Hall | C11×C37 ⋊ C4×C5 |
| Hall | C5×C11 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C37 | D11 |
| commutator, hypocenter | C11 | C4×C5×C37 |
| Frattini | C2 | C5×D11×C37 |
| Fitting, socle | C2×C5×C11×C37 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C5×C37 | |
24 conjugacy classes of subgroups.
2590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C37×Dic11, C5×C37×Dic33, C5×Dic11×C37⋊C3 |
| maximal normal subgroup of | C3×C5×C37×Dic11, C5×Dic11×C37⋊C3 |
| maximal quotient of | C3×C5×C37×Dic11, C5×C37×Dic33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 4);