Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7⋊(D43⋊C7) |
| unambiguous semidirect product | (D3×C7)⋊(D43⋊C7) |
| unambiguous semidirect product | (D3×C43⋊C7)⋊D7 |
| unambiguous semidirect product | (D3×D301)⋊C7 |
| Fitting, socle, derived | C3×C7×C43 ⋊ C22×C7 |
| Hall | C3×C7×C43⋊C7 ⋊ C22 |
| Hall | C7×C43⋊C7 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×C7×D7 |
| Sylow | C43 ⋊ D3×C7×D7 |
| Sylow | C3 ⋊ C2×C7⋊(D43⋊C7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C43 | C22×C7 |
| LCS | G ▷ C3×C7×C43 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 903 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 201);