Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20262474⋊C4 |
| derived, Sylow | C251 ⋊ C4×C25 |
| Hall | #20262474 ⋊ C4 |
| Hall | Dic251 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20262474⋊C2 |
| commutator, hypocenter | C251 | C4×C25 |
| Fitting, socle | C2×C251 | C2×C25 |
| prime radical, cosocle | C2×C251⋊C5 | C2×C5 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1004 |
Polycyclic presentation:
2,5^2,251,2|a^2=e,b^5=c,d^a=d^250,d^b=d^25,d^c=d^219110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 17);