Finite Group DatabasebetaFinite Group Databasebeta| order | 10122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D241⋊C3 |
| unambiguous semidirect product | D241⋊(C3×C7) |
| unambiguous semidirect product | (C241⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C241 ⋊ C2×C3 |
| derived, Sylow | C241 ⋊ C2×C3×C7 |
| Hall | C7×C241⋊C3 ⋊ C2 |
| Hall | C7×D241 ⋊ C3 |
| Hall | C241⋊C3 ⋊ C2×C7 |
| Hall | D241 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C241 | C2×C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
322 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11757210⋊C3, #35202290, D7×D241⋊C3, … |
| maximal normal subgroup of | C7×#11757210⋊C3, #35202290, D7×D241⋊C3, … |
| maximal quotient of | C7×Dic241⋊C3, C2×C7×D241⋊C3, C7×D241⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10122, 13);