Finite Group DatabasebetaFinite Group Databasebeta| order | 8340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C5×C139 ⋊ C22×C3 |
| Hall | D5×D139 ⋊ C3 |
| Hall | C5×C139⋊C3 ⋊ C22 |
| Hall | C139⋊C3 ⋊ C2×D5 |
| Sylow | C139 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C139 | C22×C3 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
116 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D139⋊C3, D15×D139⋊C3, D5×C3⋊(D139⋊C3), … |
| maximal normal subgroup of | C3×D5×D139⋊C3 |
| maximal quotient of | D5×D139⋊C9, C3×D5×D139⋊C3, D15×D139⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8340, 16);