Finite Group DatabasebetaFinite Group Databasebeta| order | 6820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D155 |
| unambiguous semidirect product | (C5×D11)⋊D31 |
| unambiguous semidirect product | (D11×C31)⋊D5 |
| Fitting, socle, derived, Hall | C5×C11×C31 ⋊ C22 |
| Hall | C11×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D11 |
| Sylow | C11 ⋊ C2×D155 |
| Sylow | C5 ⋊ D11×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C31 | C22 |
| LCS | G ▷ C5×C11×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
553 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊(D31⋊C3), C3×D11×D155, D11×D465, … |
| maximal normal subgroup of | D11×C5⋊(D31⋊C3), C3×D11×D155, #16811777⋊D5, … |
| maximal quotient of | C3×D11×D155, D11×D465, D33×D155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6820, 72);