Finite Group DatabasebetaFinite Group Databasebeta| order | 26265 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C103⋊C17 |
| unambiguous semidirect product | (C3×C103)⋊(C5×C17) |
| unambiguous semidirect product | (C3×C5×C103)⋊C17 |
| Fitting, socle, Hall | C3×C5×C103 ⋊ C17 |
| derived, Sylow | C103 ⋊ C3×C5×C17 |
| Hall | C5×C103 ⋊ C3×C17 |
| Hall | C3×C103 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C103⋊C17 |
| commutator, cosocle, hypocenter | C103 | C3×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C103 | C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1545 |
345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26265, 2);