Finite Group DatabasebetaFinite Group Databasebeta| order | 21414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊(D43⋊C3) |
| unambiguous semidirect product | (C43⋊C3)⋊D83 |
| unambiguous semidirect product | D3569⋊C3 |
| Fitting, socle, derived, Hall | C43×C83 ⋊ C2×C3 |
| Hall | C83×C43⋊C3 ⋊ C2 |
| Hall | D3569 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D83 |
| Sylow | C83 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C83 | C2×C3 |
| LCS | G ▷ C43×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3569 |
Polycyclic presentation:
2,3,43,83|c^a=c^42,d^a=d^82,c^b=c^36710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21414, 12);