Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C5×C139 ⋊ C2×C3 |
| derived, Sylow | C139 ⋊ C22×C3×C5 |
| Hall | C2×C5×D139 ⋊ C3 |
| Hall | C5×C139⋊C3 ⋊ C22 |
| Hall | C5×C139 ⋊ C22×C3 |
| Hall | C2×D139 ⋊ C3×C5 |
| Hall | C139⋊C3 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D139⋊C3 |
| commutator, hypocenter | C139 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
290 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×D139⋊C3, C2×C3×C5×D139⋊C3, C2×C5×C3⋊(D139⋊C3) |
| maximal normal subgroup of | C2×C3×C5×D139⋊C3 |
| maximal quotient of | C2×C5×D139⋊C9, C5×D3×D139⋊C3, C2×C3×C5×D139⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 17);