Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D139 |
| Fitting, socle, Hall | C3×C5×C139 ⋊ C22 |
| derived, Hall | C5×C139 ⋊ C22×C3 |
| Hall | C3×C139 ⋊ C2×D5 |
| Sylow | C139 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ C2×D139 |
| Sylow | C5 ⋊ C2×C3×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D139 |
| commutator, hypocenter | C5×C139 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C139 | C22 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
852 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D139⋊C9, C9×D5×D139, C3×D5×D139⋊C3, … |
| maximal normal subgroup of | D5×D139⋊C9, C9×D5×D139, C3×D5×D139⋊C3, … |
| maximal quotient of | C9×D5×D139, C32×D5×D139, C3×D15×D139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 22);