Finite Group DatabasebetaFinite Group Databasebeta| order | 16674 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C397⋊C3 |
| unambiguous semidirect product | (C2×C397)⋊(C3×C7) |
| Fitting, socle, Hall | C2×C7×C397 ⋊ C3 |
| derived, Sylow | C397 ⋊ C2×C3×C7 |
| Hall | C7×C397 ⋊ C2×C3 |
| Hall | C2×C397 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C397⋊C3 |
| commutator, cosocle, hypocenter | C397 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C397 | C3 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C2×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5558 |
1890 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7×C397⋊C3, C7×Dic397⋊C3, Dic7×C397⋊C3, … |
| maximal normal subgroup of | C4×C7×C397⋊C3, C7×Dic397⋊C3, Dic7×C397⋊C3, … |
| maximal quotient of | C4×C7×C397⋊C3, C22×C7×C397⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16674, 2);