Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D529 |
| unambiguous semidirect product | C529⋊(C2×C25) |
| Fitting, Hall | C25×C529 ⋊ C2 |
| derived, Sylow | C529 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D529 |
| commutator, hypocenter | C529 | C2×C25 |
| Frattini, socle | C5×C23 | C5×D23 |
| Fitting | C25×C529 | C2 |
| prime radical | C5×D529 | C5 |
| cosocle | C5×C529 | C2×C5 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13225 |
6650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 3);