Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20262472⋊C4 |
| derived, Sylow | C251 ⋊ C4×C25 |
| Hall | #20262472 ⋊ C4 |
| Hall | Dic251 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | D251⋊C5 |
| commutator, hypocenter | C251 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C5×C251 | C2×C5 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C5 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25100 |
Polycyclic presentation:
2,5,251,2,5|a^2=d,b^5=e,c^a=c^250,c^b=c^219350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 2);