Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C139⋊C3 |
| unambiguous semidirect product | (Dic5×C139)⋊C3 |
| derived, Hall | C5×C139 ⋊ C3×C4 |
| Hall | Dic5×C139 ⋊ C3 |
| Hall | C5×C139⋊C3 ⋊ C4 |
| Sylow | C139 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ C4×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C139⋊C3 |
| commutator, hypocenter | C5×C139 | C3×C4 |
| Fitting, socle | C2×C5×C139 | C2×C3 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic5×C139⋊C3, Dic15×C139⋊C3 |
| maximal normal subgroup of | C3×Dic5×C139⋊C3 |
| maximal quotient of | Dic5×C139⋊C9, C3×Dic5×C139⋊C3, Dic15×C139⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 11);