Finite Group DatabasebetaFinite Group Databasebeta| order | 17446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D793 |
| unambiguous semidirect product | C13⋊(C11×D61) |
| unambiguous semidirect product | C61⋊(C11×D13) |
| Fitting, socle, Hall | C11×C13×C61 ⋊ C2 |
| derived, Hall | C13×C61 ⋊ C2×C11 |
| Hall | C11×C61 ⋊ D13 |
| Hall | C11×C13 ⋊ D61 |
| Sylow | C61 ⋊ C11×D13 |
| Sylow | C13 ⋊ C11×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D793 |
| commutator, cosocle, hypocenter | C13×C61 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C61 | C2 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8723 |
4378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15691758, C11×#15691759, C11×D13×D61, … |
| maximal normal subgroup of | C11×#15691758, C11×#15691759, C11×D13×D61, … |
| maximal quotient of | C11×Dic793, C2×C11×D793 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17446, 4);