Finite Group DatabasebetaFinite Group Databasebeta| order | 10339 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C211⋊C7 |
| unambiguous semidirect product | C211⋊C72 |
| unambiguous semidirect product | (C7×C211)⋊C7 |
| Fitting, socle | C7×C211 ⋊ C7 |
| derived, Sylow | C211 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C211⋊C7 |
| commutator, cosocle, hypocenter | C211 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C211 | C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
259 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D211⋊C7, C7⋊(D211⋊C7), D7×C211⋊C7, … |
| maximal normal subgroup of | C7×D211⋊C7, C7⋊(D211⋊C7), D7×C211⋊C7, … |
| maximal quotient of | C2×C7×C211⋊C7, C3×C7×C211⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10339, 3);