Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#19104513 |
| derived, Hall | C5×#14579583 ⋊ C2 |
| Hall | #14579583 ⋊ D5 |
| Hall | C5×C172 ⋊ D9 |
| Sylow | C172 ⋊ D45 |
| Sylow | C5 ⋊ #19104513 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#14579583 | C2 |
| Frattini | C3 | C5⋊#13181892 |
| Fitting, socle | C3×C5×C172 | D3 |
| LCS | G ▷ C5×#14579583 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
Polycyclic presentation:
2,3,5,17^2,3|b^3=f^2,b^a=b^2f,c^a=c^4,e^a=de^16,f^a=f^2,d^b=d^2e^12,e^b=d^15e^14768 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 24);