Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C139 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic3×C139 |
| unambiguous semidirect product | C3⋊(C4×C5×C139) |
| derived, Sylow | C3 ⋊ C4×C5×C139 |
| Hall | C3×C5×C139 ⋊ C4 |
| Hall | C3×C139 ⋊ C4×C5 |
| Hall | C3×C5 ⋊ C4×C139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C139 | D3 |
| commutator, hypocenter | C3 | C4×C5×C139 |
| Frattini | C2 | C5×D3×C139 |
| Fitting, socle | C2×C3×C5×C139 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C139 | |
24 conjugacy classes of subgroups.
4170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic9×C139, C5×Dic3×C139⋊C3, C5×C3⋊Dic3×C139, … |
| maximal normal subgroup of | C5×Dic3×C139⋊C3, C3×C5×Dic3×C139 |
| maximal quotient of | C5×Dic9×C139, C5×C3⋊Dic3×C139, C3×C5×Dic3×C139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 6);