Finite Group DatabasebetaFinite Group Databasebeta| order | 10770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1077 |
| unambiguous semidirect product | C3⋊(C5×D359) |
| unambiguous semidirect product | C359⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C359 ⋊ C2 |
| derived, Hall | C3×C359 ⋊ C2×C5 |
| Hall | C5×C359 ⋊ D3 |
| Sylow | C359 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D359 |
| Sylow | C3 ⋊ C5×D359 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1077 |
| commutator, cosocle, hypocenter | C3×C359 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C359 | C2 |
| LCS | G ▷ C3×C359 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
2700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D359, D5×D1077, D15⋊D359, … |
| maximal normal subgroup of | C5×D3×D359, D5×D1077, D15⋊D359, … |
| maximal quotient of | C5×Dic1077, C2×C5×D1077, C5×D3231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10770, 6);