Finite Group DatabasebetaFinite Group Databasebeta| order | 13858 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | D41×C169 |
| unambiguous semidirect product | C41⋊(C2×C169) |
| Fitting, Hall | C41×C169 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D41 |
| commutator, hypocenter | C41 | C2×C169 |
| Frattini | C13 | C13×D41 |
| Fitting | C41×C169 | C2 |
| socle, cosocle | C13×C41 | C2×C13 |
| prime radical | C13×D41 | C13 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C169 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6929 |
3718 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #4223×C169, #42122969, D41×D169, … |
| maximal normal subgroup of | #4223×C169, #42122969, D41×D169, … |
| maximal quotient of | Dic41×C169, C2×D41×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13858, 3);