Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#14268588⋊C2)⋊C7 |
| unambiguous semidirect product | (#14268594⋊C7)⋊C2 |
| unambiguous semidirect product | (#14268592⋊C7)⋊C2 |
| unambiguous semidirect product | (#14268588⋊C7)⋊C2 |
| Fitting, socle, derived | C7×C43 ⋊ C22×C3×C7 |
| Hall | D7×D43⋊C7 ⋊ C3 |
| Hall | #11744749⋊C7 ⋊ C22 |
| Hall | C7×C43⋊C7 ⋊ C22×C3 |
| Sylow | C43 ⋊ C2×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C43 | C22×C3×C7 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 301 |
Polycyclic presentation:
2^2,3,7^2,43|f^a=f^42,e^b=e^6,e^c=e^2,f^c=f^36,f^d=f^41103 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 181);