Finite Group DatabasebetaFinite Group Databasebeta| order | 26650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D533 |
| unambiguous semidirect product | C13⋊(C52×D41) |
| Fitting, socle, Hall | C52×C13×C41 ⋊ C2 |
| derived, Hall | C13×C41 ⋊ C2×C52 |
| Hall | C52×C41 ⋊ D13 |
| Hall | C52×C13 ⋊ D41 |
| Sylow | C41 ⋊ C52×D13 |
| Sylow | C13 ⋊ C52×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D533 |
| commutator, cosocle, hypocenter | C13×C41 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C41 | C2 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13325 |
6700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26650, 24);