Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C139⋊C3)⋊C4 |
| unambiguous semidirect product | (C139⋊C3)⋊(C4×C5) |
| unambiguous semidirect product | Dic139⋊(C3×C5) |
| unambiguous semidirect product | (C5×Dic139)⋊C3 |
| derived, Sylow | C139 ⋊ C3×C4×C5 |
| Hall | C5×Dic139 ⋊ C3 |
| Hall | C5×C139⋊C3 ⋊ C4 |
| Hall | C5×C139 ⋊ C3×C4 |
| Hall | Dic139 ⋊ C3×C5 |
| Hall | C139⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D139⋊C3 |
| commutator, hypocenter | C139 | C3×C4×C5 |
| Frattini | C2 | C5×D139⋊C3 |
| Fitting, socle | C2×C5×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
290 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×(C139⋊C3)⋊C4, C5×C3⋊((C139⋊C3)⋊C4) |
| maximal normal subgroup of | C3×C5×(C139⋊C3)⋊C4 |
| maximal quotient of | C5×Dic139⋊C9, C3×C5×(C139⋊C3)⋊C4, C5×C3⋊((C139⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 10);