Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C5 |
| direct product | C25×C5⋊D5 |
| unambiguous semidirect product | C5⋊(D5×C25) |
| Fitting, Sylow | C52×C25 ⋊ C2 |
| derived | C52 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C25 |
| Frattini | C5 | C5×C5⋊D5 |
| Fitting | C52×C25 | C2 |
| socle, cosocle | C53 | C2×C5 |
| prime radical | C5×C5⋊D5 | C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C25 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 250 |
350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 38);