Finite Group DatabasebetaFinite Group Databasebeta| order | 21414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D249 |
| unambiguous semidirect product | C3⋊(C43×D83) |
| unambiguous semidirect product | C83⋊(D3×C43) |
| Fitting, socle, Hall | C3×C43×C83 ⋊ C2 |
| derived, Hall | C3×C83 ⋊ C2×C43 |
| Hall | C43×C83 ⋊ D3 |
| Hall | C3×C43 ⋊ D83 |
| Sylow | C83 ⋊ D3×C43 |
| Sylow | C3 ⋊ C43×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D249 |
| commutator, cosocle, hypocenter | C3×C83 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C83 | C2 |
| LCS | G ▷ C3×C83 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10707 |
5418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21414, 7);