Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C43⋊C3)⋊C4)⋊C49 |
| unambiguous semidirect product | ((C43⋊C3)⋊C49)⋊C4 |
| unambiguous semidirect product | (Dic43⋊C49)⋊C3 |
| derived, Sylow | C43 ⋊ C3×C4×C49 |
| Hall | Dic43⋊C49 ⋊ C3 |
| Hall | (C43⋊C3)⋊C49 ⋊ C4 |
| Hall | C43⋊C49 ⋊ C3×C4 |
| Hall | (C43⋊C3)⋊C4 ⋊ C49 |
| Hall | Dic43 ⋊ C3×C49 |
| Hall | C43⋊C3 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C7 | AGL(1,𝔽43) |
| commutator, hypocenter | C43 | C3×C4×C49 |
| Fitting, socle, cosocle | C2×C7×C43 | C2×C3×C7 |
| prime radical | C2×C7×C43⋊C3 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8428 |
Polycyclic presentation:
2,3,7,43,2,7|a^2=e,c^7=f,d^a=d^42,d^b=d^6,d^c=d^35602 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 2);