Finite Group DatabasebetaFinite Group Databasebeta| order | 23698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D41×C289 |
| unambiguous semidirect product | C41⋊(C2×C289) |
| Fitting, Hall | C41×C289 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D41 |
| commutator, hypocenter | C41 | C2×C289 |
| Frattini | C17 | C17×D41 |
| Fitting | C41×C289 | C2 |
| socle, cosocle | C17×C41 | C2×C17 |
| prime radical | C17×D41 | C17 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11849 |
6358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23698, 3);