Finite Group DatabasebetaFinite Group Databasebeta| order | 3346 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D239⋊C7 |
| unambiguous semidirect product | (C239⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C239 ⋊ C2×C7 |
| Hall | C239⋊C7 ⋊ C2 |
| Hall | D239 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C239 | C2×C7 |
| LCS | G ▷ C239 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 239 |
| transitive degree | μt(G) = 239 |
Polycyclic presentation:
2,7,239|c^a=c^238,c^b=c^2431 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D239⋊C7, C5⋊(D239⋊C7), C7×D239⋊C7, … |
| maximal normal subgroup of | C5×D239⋊C7, C7×D239⋊C7, C11×D239⋊C7, … |
| maximal quotient of | C5×D239⋊C7, C5⋊(D239⋊C7), D239⋊C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3346, 1);