Finite Group DatabasebetaFinite Group Databasebeta| order | 17446 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C61 · Schur multiplier (H2) = C1 |
| direct product | C13×D11×C61 |
| unambiguous semidirect product | C11⋊(C2×C13×C61) |
| Fitting, socle, Hall | C11×C13×C61 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C13×C61 |
| Hall | C11×C61 ⋊ C2×C13 |
| Hall | C11×C13 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C61 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C13×C61 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C61 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C13×C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8723 |
5551 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D11×D61, D11×D13×C61, D11×D793, … |
| maximal normal subgroup of | C13×D11×D61, D11×D13×C61, D11×D793, … |
| maximal quotient of | C13×Dic11×C61, C2×C13×D11×C61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17446, 5);