Finite Group DatabasebetaFinite Group Databasebeta| order | 21414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C83 · Schur multiplier (H2) = C1 |
| direct product | C2×C83×C43⋊C3 |
| unambiguous semidirect product | (C2×C43)⋊(C3×C83) |
| unambiguous semidirect product | (C2×C43×C83)⋊C3 |
| Fitting, socle, Hall | C2×C43×C83 ⋊ C3 |
| derived, Sylow | C43 ⋊ C2×C3×C83 |
| Hall | C43×C83 ⋊ C2×C3 |
| Hall | C2×C43 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C83 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C83 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7138 |
2822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21414, 2);