Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×Dic251⋊C5 |
| unambiguous semidirect product | Dic251⋊C52 |
| unambiguous semidirect product | (C251⋊C5)⋊(C4×C5) |
| unambiguous semidirect product | (C5×Dic251)⋊C5 |
| derived, Sylow | C251 ⋊ C4×C52 |
| Hall | C5×C251⋊C5 ⋊ C4 |
| Hall | Dic251 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D251⋊C5 |
| commutator, hypocenter | C251 | C4×C52 |
| Frattini | C2 | C5×D251⋊C5 |
| Fitting, socle | C2×C5×C251 | C2×C5 |
| prime radical | C2×C5×C251⋊C5 | C2 |
| cosocle | C2×C251 | C2×C52 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5020 |
350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 19);