Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C49 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C43⋊C3)⋊C49) |
| unambiguous semidirect product | (C22⋊(C43⋊C3))⋊C49 |
| unambiguous semidirect product | (C43⋊C49)⋊A4 |
| derived, Hall | C22×C43 ⋊ C3×C49 |
| Hall | C22×C43⋊C49 ⋊ C3 |
| Hall | C43⋊C49 ⋊ A4 |
| Hall | C22⋊(C43⋊C3) ⋊ C49 |
| Sylow | C43 ⋊ A4×C49 |
| Sylow | C22 ⋊ (C43⋊C3)⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C22⋊((C43⋊C3)⋊C7) |
| commutator, hypocenter | C22×C43 | C3×C49 |
| Fitting, socle, cosocle | C22×C7×C43 | C3×C7 |
| prime radical | C7×C22⋊(C43⋊C3) | C7 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 ◁ C7 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8428 |
Polycyclic presentation:
3,7,2^2,43,7|b^7=f,c^a=d,d^a=cd,e^a=e^36,e^b=e^41252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 35);