Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C529 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C529 |
| unambiguous semidirect product | C5⋊(D5×C529) |
| Fitting, Hall | C52×C529 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C529 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C529 |
| Frattini | C23 | C23×C5⋊D5 |
| Fitting | C52×C529 | C2 |
| socle, cosocle | C52×C23 | C2×C23 |
| prime radical | C23×C5⋊D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C529 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13225 |
7406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 9);