Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C125 · Schur multiplier (H2) = C1 |
| direct product | D5×C125 |
| unambiguous semidirect product | C5⋊(C2×C125) |
| Fitting, Sylow | C5×C125 ⋊ C2 |
| derived | C5 ⋊ C2×C125 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C125 | D5 |
| commutator, hypocenter | C5 | C2×C125 |
| Frattini | C25 | C5×D5 |
| Fitting | C5×C125 | C2 |
| socle | C52 | C2×C25 |
| prime radical | C5×D5 | C25 |
| cosocle | C5×C25 | C2×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C125 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 250 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 23);