Finite Group DatabasebetaFinite Group Databasebeta| order | 26650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D65×C41⋊C5 |
| unambiguous semidirect product | C5⋊(D13×C41⋊C5) |
| unambiguous semidirect product | C13⋊(D5×C41⋊C5) |
| unambiguous semidirect product | (C41×D65)⋊C5 |
| Fitting, socle, derived | C5×C13×C41 ⋊ C2×C5 |
| Hall | C5×C13×C41⋊C5 ⋊ C2 |
| Hall | C5×C41⋊C5 ⋊ D13 |
| Hall | C13×C41 ⋊ C5×D5 |
| Sylow | C41 ⋊ C5×D65 |
| Sylow | C13 ⋊ D5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C41 | C2×C5 |
| LCS | G ▷ C5×C13×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2665 |
442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26650, 20);