Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C17 |
| direct product | C5×D3×C172⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C5×C172⋊C3) |
| unambiguous semidirect product | (D3×C172)⋊(C3×C5) |
| unambiguous semidirect product | (C5×D3×C172)⋊C3 |
| Fitting, socle | C3×C5×C172 ⋊ C2×C3 |
| derived | C3×C172 ⋊ C2×C3×C5 |
| Hall | C3×C5×C172⋊C3 ⋊ C2 |
| Hall | C3×C172⋊C3 ⋊ C2×C5 |
| Hall | C5×C172 ⋊ C3×D3 |
| Sylow | C172 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×C172⋊C3 |
| commutator, cosocle, hypocenter | C3×C172 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C2×C3 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 ◁ C5 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 51);