Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic43⋊C49) |
| unambiguous semidirect product | Dic129⋊C49 |
| unambiguous semidirect product | (C43⋊C49)⋊Dic3 |
| derived, Hall | C3×C43 ⋊ C4×C49 |
| Hall | C3×C43⋊C49 ⋊ C4 |
| Hall | C43⋊C49 ⋊ Dic3 |
| Hall | Dic129 ⋊ C49 |
| Sylow | C43 ⋊ Dic3×C49 |
| Sylow | C3 ⋊ Dic43⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C7 | C3⋊(D43⋊C7) |
| commutator, hypocenter | C3×C43 | C4×C49 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C43 | C2×C7 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25284 |
Polycyclic presentation:
2,7,3,43,2,7|a^2=e,b^7=f,c^a=c^2,d^a=d^42,d^b=d^35420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 6);