Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C17 |
| direct product | C5×#19104523 |
| Fitting, socle, Hall | C5×C172 ⋊ C2×C9 |
| derived, Sylow | C172 ⋊ C2×C5×C9 |
| Hall | C5×#14579585 ⋊ C2 |
| Hall | C5×C17⋊D17 ⋊ C9 |
| Hall | #14579585 ⋊ C2×C5 |
| Hall | C17⋊D17 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #19104523 |
| commutator, hypocenter | C172 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C172 | C2×C9 |
| prime radical | C5×(C17⋊D17)⋊C3 | C3 |
| cosocle | C172⋊C3 | C2×C3×C5 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 41);