Finite Group DatabasebetaFinite Group Databasebeta| order | 21414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3569 |
| unambiguous semidirect product | C83⋊(C3×D43) |
| Fitting, socle, Hall | C3×C43×C83 ⋊ C2 |
| derived, Hall | C43×C83 ⋊ C2×C3 |
| Hall | C3×C83 ⋊ D43 |
| Hall | C3×C43 ⋊ D83 |
| Sylow | C83 ⋊ C3×D43 |
| Sylow | C43 ⋊ C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3569 |
| commutator, cosocle, hypocenter | C43×C83 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C83 | C2 |
| LCS | G ▷ C43×C83 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10707 |
5358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21414, 5);