Finite Group DatabasebetaFinite Group Databasebeta| order | 10740 |
| automorphism | Aut(G) order 7646880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5370 |
| direct product | C2×D2685 |
| unambiguous semidirect product | (C2×C3)⋊D895 |
| unambiguous semidirect product | (C2×C5)⋊D537 |
| unambiguous semidirect product | (C2×C179)⋊D15 |
| Fitting, socle | C2×C3×C5×C179 ⋊ C2 |
| derived, Hall | C3×C5×C179 ⋊ C22 |
| Hall | C5×C179 ⋊ C2×D3 |
| Hall | C3×C179 ⋊ C2×D5 |
| Sylow | C179 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D179 |
| Sylow | C5 ⋊ C2×D537 |
| Sylow | C3 ⋊ C2×D895 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2685 |
| commutator, cosocle, hypocenter | C3×C5×C179 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C179 | C2 |
| LCS | G ▷ C3×C5×C179 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D8055, D3×D2685, C2×C3×D2685, … |
| maximal normal subgroup of | C2×C3×D2685, D10740 |
| maximal quotient of | C2×D8055, D3×D2685, C2×C3×D2685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10740, 22);