Finite Group DatabasebetaFinite Group Databasebeta| order | 3346 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C239⋊C7 |
| unambiguous semidirect product | (C2×C239)⋊C7 |
| Fitting, socle, Hall | C2×C239 ⋊ C7 |
| derived, Sylow | C239 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C239⋊C7 |
| commutator, cosocle, hypocenter | C239 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C239 | C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 241 |
| transitive degree | μt(G) = 478 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C239⋊C7, D5×C239⋊C7, D7×C239⋊C7, … |
| maximal normal subgroup of | C2×C5×C239⋊C7, C2×C7×C239⋊C7, C2×C11×C239⋊C7, … |
| maximal quotient of | C2×C5×C239⋊C7, D5×C239⋊C7, C2×C239⋊C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3346, 2);