Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C5⋊#19104514 |
| derived, Hall | C5×C172 ⋊ C2×C9 |
| Hall | C5×#14579583 ⋊ C2 |
| Hall | C5⋊(C17⋊D17) ⋊ C9 |
| Hall | #14579583 ⋊ D5 |
| Sylow | C172 ⋊ C9×D5 |
| Sylow | C5 ⋊ #19104514 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊((C17⋊D17)⋊C3) |
| commutator, hypocenter | C5×C172 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C172 | C2×C3 |
| prime radical | C3×C5⋊(C17⋊D17) | C3 |
| LCS | G ▷ C5×C172 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
Polycyclic presentation:
2,3,5,17^2,3|b^3=f,c^a=c^4,d^a=d^16,e^a=e^16,d^b=d^2e^16,e^b=d^7e^14756 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 25);