Finite Group DatabasebetaFinite Group Databasebeta| order | 13858 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C41 · Schur multiplier (H2) = C1 |
| direct product | C13×D13×C41 |
| unambiguous semidirect product | C13⋊(C2×C13×C41) |
| Fitting, socle, Hall | C132×C41 ⋊ C2 |
| derived | C13 ⋊ C2×C13×C41 |
| Sylow | C132 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C41 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C13×C41 |
| Frattini | C1 | G |
| Fitting, socle | C132×C41 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C41 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1066 |
4264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D13×D41, C13×C41×#261, C13×#14523823, … |
| maximal normal subgroup of | C13×D13×D41, C13×C41×#261, C13×#14523823, … |
| maximal quotient of | C13×C41×Dic13, C2×C13×D13×C41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13858, 9);