Finite Group DatabasebetaFinite Group Databasebeta| order | 10740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D895 |
| unambiguous semidirect product | (C5×D3)⋊D179 |
| unambiguous semidirect product | (D3×C179)⋊D5 |
| Fitting, socle, derived, Hall | C3×C5×C179 ⋊ C22 |
| Hall | C5×C179 ⋊ C2×D3 |
| Hall | C3×C179 ⋊ C2×D5 |
| Sylow | C179 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D179 |
| Sylow | C5 ⋊ D3×D179 |
| Sylow | C3 ⋊ C2×D895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C179 | C22 |
| LCS | G ▷ C3×C5×C179 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1347 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D895, C3×D3×D895, D3×D2685, … |
| maximal normal subgroup of | C3×D3×D895 |
| maximal quotient of | D9×D895, C3×D3×D895, D3×D2685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10740, 19);