Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D417 |
| unambiguous semidirect product | (C3×D5)⋊D139 |
| unambiguous semidirect product | (D5×C139)⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C139 ⋊ C22 |
| Hall | C5×C139 ⋊ C2×D3 |
| Hall | C3×C139 ⋊ C2×D5 |
| Sylow | C139 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D139 |
| Sylow | C5 ⋊ C2×D417 |
| Sylow | C3 ⋊ D5×D139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C139 | C22 |
| LCS | G ▷ C3×C5×C139 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
840 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D1251, D5×C3⋊(D139⋊C3), C3×D5×D417, … |
| maximal normal subgroup of | D5×C3⋊(D139⋊C3), C3×D5×D417 |
| maximal quotient of | D5×D1251, C3×D5×D417, D15×D417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 28);