Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C5⋊#13181892 |
| unambiguous semidirect product | C5⋊(C3×#13181892) |
| Fitting, socle | C3×C5×C172 ⋊ D3 |
| derived | C5×C172⋊C3 ⋊ C2×C3 |
| Hall | C3×C5×C172⋊C3 ⋊ C2 |
| Hall | C3×C172⋊C3 ⋊ D5 |
| Hall | C5×C172 ⋊ C3×D3 |
| Sylow | C172 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3×#13181892 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊#13181892 |
| commutator, cosocle, hypocenter | C5×C172⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | D3 |
| LCS | G ▷ C5×C172⋊C3 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
819 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 49);