Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C251⋊C5)⋊Dic5 |
| unambiguous semidirect product | Dic1255⋊C5 |
| derived | C5×C251 ⋊ C4×C5 |
| Hall | C5×C251⋊C5 ⋊ C4 |
| Sylow | C251 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D251⋊C5) |
| commutator, hypocenter | C5×C251 | C4×C5 |
| Fitting, socle, cosocle | C2×C5×C251 | C2×C5 |
| prime radical | C2×C5×C251⋊C5 | C2 |
| LCS | G ▷ C5×C251 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5020 |
Polycyclic presentation:
2,5^2,251,2|a^2=e,c^a=c^4,d^a=d^250,d^b=d^219290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 20);