Finite Group DatabasebetaFinite Group Databasebeta| order | 7860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(D131⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(D131⋊C5) |
| unambiguous semidirect product | (C2×C131⋊C5)⋊D3 |
| unambiguous semidirect product | (C2×D393)⋊C5 |
| Fitting, socle | C2×C3×C131 ⋊ C2×C5 |
| derived, Hall | C3×C131 ⋊ C22×C5 |
| Hall | C3×C131⋊C5 ⋊ C22 |
| Hall | C2×D393 ⋊ C5 |
| Hall | C131⋊C5 ⋊ C2×D3 |
| Sylow | C131 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C2×D131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(D131⋊C5) |
| commutator, hypocenter | C3×C131 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C131 | C2×C5 |
| LCS | G ▷ C3×C131 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9⋊(D131⋊C5), D3×C3⋊(D131⋊C5), C2×C3×C3⋊(D131⋊C5), … |
| maximal normal subgroup of | C2×C3×C3⋊(D131⋊C5) |
| maximal quotient of | C2×C9⋊(D131⋊C5), D3×C3⋊(D131⋊C5), C2×C3×C3⋊(D131⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7860, 17);