Finite Group DatabasebetaFinite Group Databasebeta| order | 26650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D13×C41⋊C5 |
| unambiguous semidirect product | C13⋊(C2×C5×C41⋊C5) |
| unambiguous semidirect product | (D13×C41)⋊C52 |
| unambiguous semidirect product | (C5×D13×C41)⋊C5 |
| Fitting, socle | C5×C13×C41 ⋊ C2×C5 |
| derived, Hall | C13×C41 ⋊ C2×C52 |
| Hall | C5×C13×C41⋊C5 ⋊ C2 |
| Hall | D13×C41 ⋊ C52 |
| Sylow | C41 ⋊ C52×D13 |
| Sylow | C13 ⋊ C2×C5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D13×C41⋊C5 |
| commutator, cosocle, hypocenter | C13×C41 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C41 | C2×C5 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2665 |
520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26650, 16);