Finite Group DatabasebetaFinite Group Databasebeta| order | 13842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D769 |
| Fitting, Hall | C9×C769 ⋊ C2 |
| derived, Sylow | C769 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D769 |
| commutator, hypocenter | C769 | C2×C9 |
| Frattini | C3 | C3×D769 |
| Fitting | C9×C769 | C2 |
| socle, cosocle | C3×C769 | C2×C3 |
| prime radical | C3×D769 | C3 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6921 |
3474 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#15690484, C9⋊#15690484, D9×D769, … |
| maximal normal subgroup of | C9×#15690484, C9⋊#15690484, D9×D769, … |
| maximal quotient of | C9×Dic769, C2×C9×D769 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13842, 5);