Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| automorphism | Aut(G) order 9512800 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5170 |
| direct product | C2×D2585 |
| unambiguous semidirect product | (C2×C5)⋊D517 |
| unambiguous semidirect product | (C2×C11)⋊D235 |
| unambiguous semidirect product | (C2×C47)⋊D55 |
| Fitting, socle | C2×C5×C11×C47 ⋊ C2 |
| derived, Hall | C5×C11×C47 ⋊ C22 |
| Hall | C11×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D55 |
| Sylow | C11 ⋊ C2×D235 |
| Sylow | C5 ⋊ C2×D517 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2585 |
| commutator, cosocle, hypocenter | C5×C11×C47 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C47 | C2 |
| LCS | G ▷ C5×C11×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2585, C2×C3×D2585, C2×D7755, … |
| maximal normal subgroup of | C2×C3×D2585, D10340 |
| maximal quotient of | D3×D2585, C2×C3×D2585, C2×D7755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 30);