Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊C5×D47 |
| unambiguous semidirect product | C47⋊(C22×C11⋊C5) |
| unambiguous semidirect product | (C2×C47)⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C2×C11×D47)⋊C5 |
| Fitting, socle | C2×C11×C47 ⋊ C2×C5 |
| derived, Hall | C11×C47 ⋊ C22×C5 |
| Hall | C47×C11⋊C5 ⋊ C22 |
| Hall | C2×C11×D47 ⋊ C5 |
| Sylow | C47 ⋊ C22×C11⋊C5 |
| Sylow | C11 ⋊ C2×C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊C5×D47 |
| commutator, cosocle, hypocenter | C11×C47 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C47 | C2×C5 |
| LCS | G ▷ C11×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C11⋊C5×D47, C2×C3×C11⋊C5×D47, C2×C11⋊C5×D141 |
| maximal normal subgroup of | C2×C3×C11⋊C5×D47 |
| maximal quotient of | D3×C11⋊C5×D47, C2×C3×C11⋊C5×D47, C2×C11⋊C5×D141 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 17);