Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C251⋊C5 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C251)⋊C5 |
| Fitting, socle, derived | C5×C251 ⋊ C4×C5 |
| Hall | C5×C251⋊C5 ⋊ C4 |
| Sylow | C251 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C251 | C4×C5 |
| prime radical | D5×C251⋊C5 | C2 |
| cosocle | D5×C251 | C2×C5 |
| LCS | G ▷ C5×C251 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1255 |
275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 32);